Other than riding dragons into battle and using slaves to mine their riches, valyrians were also famous for the materials used in both their weapons, ornaments, armor and structures ( amongst other things ). They were known for adding magical properties to these materials through the use of spells whilst forging. Valyrian Steel is a magical alloy ( a mixture of metal with different elements, but metal remains the base and principal one ) that when used for weapons, the quality of the swords was unparalleled, lighter than any others but stronger and sharper as well, able of holding an edge ( forever ) without any need for maintenance. The steel has a distinctive rippled pattern ( the product of being folded on itself many times over ) and is dark-grey in color. The secrets of how to forge this metal was lost in the Doom of Valyria but there are those very few who can reforge an already existing blade into another weapon ( such as the great sword Ice was reforged into two longswords; Widow's Wail and Oathkeeper ). Other such objects made from Valyrian Steel is Aegon the Conqueror's crown, several many other blades ( many lost ), steel links that some maesters wear on their collars, and even a dragon horn found by Euron Greyjoy that's banded with the steel.

Dragonstone ( again, not the castle or island ) is a material that valyrians used in their construction, which was also worked with spells. It's a black stone material that's harder than steel and diamond. The castle of Dragonstone on the island by the same name, the Black Walls of Volantis and the Valyrian Roads or Dragonroads are amongst these constructions. It is not to be confused with Dragonglass nor the Black Stone that can be found in other structures around the known world ( the latter such in places as Asshai and the Shadow Lands ), which is oily to the touch, unlike Dragonstone.

And then we have Dragonglass or Frozen Fire as valyrians would call it, also known as obsidian. Now, unlike in our world, the obsidian of ASOIAF has magical properties that valyrians were known to use in artifacts, such as the infamous glass candles that burn with a strange light ( if they burn, that is ). These glass candles had the ability to project thoughts, images and the like across vast distances almost instantaneously, which was the main way of communication between the cities of the Freehold with the capitol in the valyrian peninsula ( it's how Volantis called for help when the Rhoynar were at war with them ). Not only that, but the users could invade another's dreams as well, all when the candles burned. The tricky part is getting them to burn but more on that below.

Valyrian Steel

As was remarked earlier, the secrets to how valyrians forged the magical metal is lost but since this is a headcanon of a knowledge that Vaedar ( in his dragonlord verses ) knows, then I will proceed to explain as uncomplicated as possible.

One of the things needed in order to work with this magical alloy is dragonfire. Dragons have long been associated with magic and it's no surprise to think that their fire itself has magical capabilities. Although the regular fire that smiths use such as those in Qarth that swear to know the secrets of working the metal, can indeed reheat and remelt it enough to allow reforging of the steel, it only serves as a conduct to manipulate something that is already created. Dragonfire has the components to be paired with the spells in order to give it its legendary edge on blades and for these spells to be powered, blood sacrifices would be done. Valyrian Steel is also distinct from others due to the ripple patterns of it, which are never the same from one piece to another. This in part is due to the many times the metal is folded ( which has many complex things that also add to the pattern ) on itself along with the spells utilized in the process of doing so.

I researched a little on real life metals that have similar characteristics to those of Valyrian Steel and the most evident that came up was Damascus Steel. Some of the similarities include that the original method by which the steel was forged is not known and also like Valyrian Steel, there are those who claim to have rediscovered said method. Damascus Steel holds an edge that gave rise to legendary feats, and it's both 'flexible' to absorb impact beyond the breaking point but also very hard. It's known that some forms of biomass elements were used in the carburization process ( a way in which carbon is absorbed by metal basically, through heat ), and gave way to intricate and complex components into the alloy that make it so that if any detail of them is altered too much, the result may be different. There are modern ways to work Damascus Steel but they do not match the original way done so centuries ago.

It is based on this knowledge that I managed to wrap my head around enough to understand the basics of it, that I came up with a headcanon process of how Valyrian Steel was forged, associating it with the components of the Damascus. The biomass element would be found in both the dragonfire and the blood of those sacrificed, as well as the spells that would bring it together, which means that I am using the 'biomass' as an equivalent to the magic that exists in ASOIAF. The hotter the fire, the more it absorbs, the harder the metal. This way, it makes those without intimate knowledge of valyrians and their magic ( and the use of it ) unable to forge the legendary, magical alloy.

Vaedar in his dragonlord verses, has a Valyrian Steel sword of his own called Strife. Over here ( http://vaedar.tumblr.com/post/167599910962/excuse-the-little-bent-position-i-didnt-use ) is a drawing I once made of it and plan to remake in digital sometime.

DRAGONSTONE / FUSED STONE

Dragonstone is a black stone material valyrians used in their constructions. It's known to be harder than steel and diamond, and was worked with the use of magical spells. Not much at all is known of this stone other than that, but its appearance is very similar to even older structures and ruins throughout the known world, although the Black Stone being referred to now is oily, where areas the Dragonstone was drier. Both, however, seem to be built similarly ( blocks of stone that were not put together but rather molded into shape ). This is where the connection between Valyrians and the Great Empire of the Dawn's construction techniques comes. Valyrians were capable of shaping the stone with unparalleled skill thanks to their magical prowess, decorating their buildings with all sorts of formations and statues as ornaments. 

Like Valyrian Steel, dragonfire ( likely maybe even blood, as was rumored to be used in real life Roman concrete ) has an important role to play in the construction for along with spells, it heats the stone enough to shape it. The stone has the faint echo of the magic used in its construction still lingering within. It is likely that the Black Stone and Dragonstone are either different variations or the same construction methods or actually the same but valyrians altered it; or that the oily black stone is a 'corrupted' or poisoned fused stone ( following some cataclysm or magical fallout such as a power dark spell ). The topless towers and many other roads and bridges in the city of Valyria were almost in their totality made of this stone, for it could withstand the somewhat harsher conditions of the peninsula due to the presence of the Fourteen Flames. The Black Walls of Volantis, Dragonstone ( the castle ) and the Dragon Roads are all made of the same material, constructed by valyrians.

DRAGONGLASS 

Also known as Frozen Fire by the valyrians, Dragonglass is a magical volcanic glass or obsidian that was favored by valyrians and the Children of the Forest for different uses. This glass formation some believe is made by dragons themselves while the maesters conclude that it's from the fires of the earth. Due to the presence of its formations in places were volcanic activity occurs, the latter is likely correct ( In our world, that is how obsidian is created, of course ). Places like Dragonstone where the Dragonmont is semi-active, large deposits of the glass can be found. During the time of the Freehold, the valyrian peninsula had the largest deposit thanks to the presence of the Fourteen Flames, so valyrians had access to great amounts of this glass. One of the more famous in which they utilized it, was in their glass candles.

These candles that may come in different color variations ( as does the dragonglass but they all have a dark hue to the colors ) were used as a means of communication ( primarily ). Users on different corners of the world could communicate instantly, which came very handy during wars and other events in which the long waits for ravens or horses to arrive could determine victory or defeat. But how was it possible? The glass candles are made of Dragonglass which as stated before, has magical characteristics in the ASOIAF world. However, this magic took effect only when the candles burned so it's easy to associate a relation between the magic and the fire, and in turn, with dragons. Glass candles have not burned for a century which is near the time dragons went extinct in the known world and with the death of the last dragon, it is believed that magic itself grew weaker or maybe even disappeared. Until Daenerys brought them back, which is then that the glass candles start to burn again.

In this matter, I will go with the glass candles burning in response to magic, which means that magic must be used in order to have them burn and thus, use its strange powers. And since all valyrian magic was based on fire and/or blood, then it's easy to conclude that blood would've been used to activate the candles, such as a prick of the skin against one of the jagged edges of the candle. Through the glass candle, the user can communicate with another person through thoughts and visions. It's very likely that Quaithe is communicating with Daenerys through the use of a glass candle in the books so it means that the receiver of said message doesn't necessarily have to be in the presence of a glass candle if the user is able of invading the mind of the person they want to contact. We can assume that for this to work, the person must be skilled enough in magic but it seems that the candles may light up by themselves ( as it's being reported is happening ), through the presence of magic ( if we go with the rebirth of dragons meaning the rebirth or strengthening of magic in the world, along with the coming of the Others ).

Another way I've been playing about with the candles is that they serve as a form of conduit or an amplifier of sorts for the magic of the user, which that way, would explain why it's possible to get in contact with another person through vast distances without that other person being in front of a glass candle ( as Quaithe did with Dany ). This would mean that the glass candles could have other uses aside from those of communication. As with all magic, it's not known specifically how these artifacts are supposed to work or the potential they have, and the same goes to the material itself; the Dragonglass.

The Children of the Forest used the glass as weapons because it's sharper than steel ( which they did not know how to work ) but it's very brittle or easy to break ( like glass ). But only this material is a confirmed, known weakness against the Others and the Children once faced them in battle ( along with First Men ) and managed to drive them back to the Lands of Always Winter, building The Wall as protection afterwards. It's safe to conclude that this material is indeed a magical glass, and the term 'frozen fire' used by valyrians is quite literal in its sense for it's the result of the volcanic activity beneath the earth's surface, when lava is cooled very quickly ( though of course, specific components in the chemical composition need to be present in order for obsidian to be formed ).