Use Pan/Crop to move the text in or out, or you can keyframe the text in/out on it's own. You could also use track motion as well, but again, it involves keyframes.

Place the audio you want on the timeline, then put the cursor where you want the audio to come in. Press the S key to split it. Delete the audio coming before the split point. Now find where you want the audio to end. Press the S key again to split. Delete what comes after the split point. Now you're left with a small chunk of audio, and you'll have what you want.
You could also use a volume envelope to bring in/out sound, kinda like a fader control on a mixer. Highlight the audio you want by clicking on it, press the "V" key to insert a little blue line. Double click the line to add volume points. Pull em' down to make the audio go away, slide em' up to bring the audio back in.