Cut
This is the most commonly used transition used in editing where two shots are being joined. Its very basic in the way that you join these two shots and there is not technical processes to go through joining the cuts. When editing the film strips are placed together and when played the shots play one after the other.
Dissolve
A dissolve is gradual fade from one shot to another. They can be used to link two different objects, and one shot gradually fades into the next. The dissolve overlaps the two shots while the effect is taking place, which can also be used in montage sequences.
Fade
A fade takes place when a shot is fading out, usually to a single colour which is mostly black. Fade ins usually occur at the beginning of films to symbolise something coming into shot, and fade outs are used mostly when a film is ending, to signify something ending.
Wipe
A wipe involves one shot replacing another, from one side of the frame to another. A way to remember how this works is to imagine a vertical passing through the frame from right to left. The left side is A and the right side is B. On the left side of this line, we have shot A, and on the right side of this line is shot B. When this line reaches the left edge of the frame, shot B will completely fill the scene, and the transition is complete.