Once you reach level 30, you’ll receive a letter in the mail regarding Ascalonian Catacombs, the first dungeon that you’ll have access to. The most important thing to keep in mind for dungeons is that they were implemented at launch and there weren’t too many updates to them over the years.
All future 5-man content revolves around story missions (fairly easy, but enjoyable) and fractals, which are very fun and challenging due to a system that includes four tiers of difficulty. You’re able to enter fractals at any level and it will scale you up to level 80. You won’t be as strong as a regular level 80 character, but you’ll be able to complete Tier 1 Fractals that don’t require agony. I recommend doing this with guildies or friends, as pick up groups might not take too kindly to you if you’re below level 80. Please review the fractals section for additional information.
Despite this, I feel that dungeons are still very much worth doing and are a fun activity to complete with friends, guildmates, or even in (some) pick-up groups. In addition, the story mode of dungeons explain what Destiny’s Edge is up to while you complete your personal story.
If you look at the below list of dungeons, you’ll notice that there are separate story and explorable modes for each dungeon. There is a drastic difference in difficulty between the two modes and while the story mode is easier, it tends to take longer to complete. Most people will be able to complete the story mode of a dungeon with three relatively inexperienced players, while groups of five inexperienced players might have a difficult time completing explorable paths of the dungeons. Most dungeons have three explorable paths that will tell a different story in addition to providing different encounters/bosses. Explorable paths will grant dungeon currency when completed, which may be exchanged here for weapons/armor and other things required to craft certain items.
My advice is to use the Looking for Group tool (Default key: Y) to start your own dungeon group if you’re interested in completing one and don’t have friends/guildmates to play with. Clearly state in the group name that you’re looking to complete Story with all cutscenes (ex. AC story all cutscenes) or if you’re looking to complete an explorable path, state that you’re new to it (ex. AC p1 first time). This will save you and other players from frustration if they’re looking to speedrun it with people who are aware of the fastest methods to complete the dungeon.
I also recommend using gw2dungeons.net to familiarize yourself with explorable paths before running them or at least using it as a resource if your group is having trouble.