To answer the original question;
Highlight the setion you want to move.
Hold CTRL button and while holding, use the mouse to grab the track and slide it a bit.

If you need to be really exact simply highlight the section, then zoom in in either the Tracks or Audio Edit window before grabbing and sliding it.

For example, you can often look at a given peak that should be 'on the beat'.
Zoom way in and then slide the peak to be in line with what you want.

Tip: It is possible to set the 'Now' cursor point on the main window so you have a reference point. In either the Audio Edit window or the Tacks window, once zoomed in, click the timeline at the top. This sets a 'Now' point that can be referenced when sliding the track.
Set Now 'right on the beat' and then drag the track until the peak lines up with 'Now' line set earlier.

Next level user tip:
You'll learn that when dragging the audio when zoomed in can result in it still being 'off' by a little bit. This is because of 'Resolution'. This is found under Options menu.

PG Products (including PT) default to resolution 120.
Set it up as high as your system allows.
This is the setting for how 'fine' an adjustment can be. 120 is the number of times you can divide each beat.
If the tempo is 120 (a half second per beat) this is by default set at 500 ms per beat.
So you can divide 500 ms by 120 and that tells you hos close (in ms) you can get with your audio edits.

When you need more accurate results, you can set the Resolution at 3840 usually with no problem .. then you can nudge a track within 0.13 ms versus 4 ms at default settings.
This setting has very little effect on system resources or file size so there's really no reason not to use it.
For what it's worth this settings does affect audio edits as well as MIDI, so worth mentioning.

I do not work here, but the benefits are still awesome
Make your sound your own!