This free sample chapter from the Premiere Pro CS5 Classroom in a Book teaches how to do simple video edits:
There are more sample chapters from that book and links to other basic information here.
See this page (and the tutorials that it links to) for information about transitions and how to apply them:
This page is a good starting point for learning Premiere Pro.
If the clip is already in your timeline, go ahead and just use the razor tool and delete the sections you don't want.
If the clip is in your source monitor, you can set in / out points and bring individual pre-determined clips from the source monitor and drag them onto your timeline. This is the method I prefer if its a longer clip.
I agree with Todd, and cannot recommend CiaB PrPro CS5, Adobe Press too highly.
You already have the main concepts of video editing, and all that you need to do is translate that knowledge from PrE's interface, to CS5. That book will take you on a guided tour of where things are located, and how to use them in PrPro. Once you get the "lay of the land," it will be an easy transition.
The concepts are the same between the two programs, but the mechanics of many aspects are different, and there is more to consider with PrPro. Pick up a copy of CiaB, and work through the exercises, from start to finish. You will not regret it.