Cut - The simple cut is the most commonly used transition in filmmaking. Back when most editing was done with physical film, the cut would've been a literal cut, where the film strip is cut at the necessary moment in the shot, then taped to the next film strip where the next moment was to begin. With digital film making, the cuts are made by creating references to particular moments in the digital file, then telling the software to sequence them. These instructions are then used to write the final file in the export. 

Straight forward cuts might be the only transition you'll ever use. If timed correctly they can appear smooth and seamless, or can provide dynamic or sharp moments, or even rhythm and musicality to your video. 

Cuts tend to appear smoother when timed with the movement in the scene, cutting on action is a very common technique for example, but also when they are coordinated with the audio. 

Cutting both visuals and audio at the same time can create a harsh cut due to the change in background audio such as changes in room tone or music, or even changes to the sound created by different cameras, microphones & distances. This effect could be used creatively at key moments, but generally having a continuous source of audio such as an audio track can assist cuts to look smooth & seamless, or coordinated with the music. Even having a background track, this could be music, atmospheric sounds or room tone, as a layer underneath can help to smooth out variations in audio quality between sources, as well as enhancing the mood of your piece. 

Finding your editing 'rhythm' is often quite personal and takes practice, and it's very hard to explain why certain cuts feel right and others don't, it will just come with practice. 

Cross-Dissolve / Cross-Fade - These types of transitions have a moment where two source of video are played simultaneously as one fades out and the next fades in. 

These types of transitions can be applied in different speeds, but generally have a smoother feel to straight cuts. They can be used to accentuate mood or tone, for example during and edit of a slow song you might use lots of cross-dissolves to compliment the flow of the piece. They can also help to transition us more smoothly from two states which are quite different, where a cut might feel too sharp too harsh. They can also be useful at the beginning and end of a piece to bring us gently in or out of the piece, from text for example. 

Cross-dissolves usually also fade the audio as well as the visuals, which also helps to make the transition feel smoother. They would therefor be useful to use when transitioning between two scenes with very different audio states. 

They can be used throughout an edit in combination with cuts without disrupting the flow. 

Fade to Colour (Usually black) - A fade to colour, or fade to black depending on the editor, is where the clip will fade out to black, and then from black fade into the next clip, or if no clip follows, remain in black. 

They give us a moment to absorb the previous image before moving immediately onto the next one. They can also be useful for linking visual information from different types of scenes, and as such can also be used to divide a video into sections. 

These types of fades are used extensively in trailers, as they can link different types of visual information, but can also be used to tease the viewer with hints of a scene or in varying rhythms to generate tension, etc. 

These type of transitions function similarly to cross dissolves, and as such the effect is also applied to the audio. 

They can also be useful at the beginning and end of a piece to bring us gently in or out of the piece. 

J-Cut / L-Cut - These types of cuts are the result of the video and audio transitioning at different times. In a J-Cut the audio will begin to appear before the visuals are revealed, in an L-Cut the audio will continue on for longer after the visuals have changed to another scene. Both the video and audio in either incidence can be cut or faded.

These types of cuts are not available in all editors, but the effects can be replicated when the video is placed in different layers. 

They really help the flow of your audio and visual elements to feel seamless, and help you to build your soundscape. 

Creative - There are many different creative transition types available in most editors and these animate your video in many various ways. 

They generally create a bigger feeling of change, so are most effective when used sparingly such as at the beginning and end or between sections. When the same creative transition is used several times it will help to build your aesthetic, using lots of different transition types can often feel quite messy and confusing. Creative transitions should be chose carefully to compliment the tone of your video. 

Creative transitions can also be applied to text using most editors, and when used in this way the transitions feel more like animated graphics. They have more of an impact when the effects are applied to video. 

Creative transitions can be very effective for content such as trailers or short overview videos for events and performances.