Adobe Premiere has several different ways to adjust your clip to fit your specifications. Note that on this page we are just giving you the bare minimum--the information you need to edit one clip. More complex editing options are available, we just don't have space to explain them here.
What follows are a few ways to edit your clip.
You can use this option with either end of the clip. Note: You will not be able to use the trim option to extend your clip past its original capture length--only to shorten it.
Get your clip to the point you want to cut. To do this, play from the timeline (use the spacebar to start and stop). To get your cursor to a more precise moment, use the slider-bar in the target screen to adjust by frame.
When you have your clip where you want it, select the Razor tool and click on the cursor line. Your clip will split and a new icon will appear in the clip to the right. This tells you that the clips are now two different clips.
Finally, choose the select tool (an arrow, top row, left corner) and select the portion of your original clip you don't want. Press "Delete" and you are done. Note: if you are using both video and sound, be sure to delete the sound portion of your clip too.
Select the in (or out) tool (bottom, right corner of the tool palette). Be sure you have the tool you want (clicking the "in" tool at the point you want to be the "out" marker would not be good). Now, simply click on the moment you've chosen. You will notice that rather than splitting into two clips, the part 'outside' your marker simply disappears.