Video transitions are absolutely crucial when editing together digital video projects of reasonable length. They give a sense of time and mood changes and really allow scenes and situations to be broken up.
You can begin using video transitions when you have two video clips lined back to back in your Timeline. Go to the Browser, and then click on the Effects tab. Click on the Video Transitions folder and you will be given a list of video transition groupings, like dissolves and wipes. These are all different types of transitions that are available, but the most common to use are dissolves. Click on the dissolve folder to be given the full selection of dissolves to be used. This will range from things like fade in and fade outs, to cross-dissolves that simply fade one image into another. You then take the dissolve you would like to use, drag it from the Browser to the Timeline, and drop it at the end of the first clip. Then if you want the same dissolve for the entry of the second clip you drag and drop it on the front part of the second clip. If you are using a cross dissolve you simply drag and drop the dissolve between the two clips, and the transition will be distributed equally on each clip. Once the transition or transitions are applied to the clips you can shorten or lengthen them depending on how slow or fast you want them to be. Certain dissolves, like the fade in and fade out, require a small bit of space in between the clips so it is possible to fade to black between them. In this case you may have to split the clips apart just slightly.
There are many other types of transitions available in Final Cut Pro, including classic wipes and irises that were used in the silent film era. There are even more animated “3D" transitions that will let the image blow up into another one or “wash away." The simpler choice is often the best one because you usually want the attention to be on the story in your project rather than the transition effects. The principle is relatively the same no matter what effect you are using. Simply drag the transition you want onto the ends of the two clips you want to transition into each other, and then adjust their length to make sure it looks correct. Once you get the hang of this it will begin to be a fairly intuitive process.