Most ranges have a basic safety course, and this usually includes hands-on time on the range. Make sure it's an NRA Certified instructor (it's easy enough to qualify as such, and is a de-facto national standard - anyone who is passing themselves off as an instructor who is not NRA Certified is someone to avoid).

In NoVA there are quite a few indoor pistol ranges, so it's more a question of convenience. WhereToShoot.org is a good starting point to find something close to you.

Now, if you are not a beginner, well.... what are you looking to shoot? Clark Bro's in Warrenton is unlimited range time - but you have to buy the ammo there; longest range is, IIRC, about 50 yards (plenty for pistol, but cramped for rifle). Peacemaker goes out to 1000 yards, but it's well out into WV. Quantico also has 1000 yards, but you have to be a member (and membership is not straightforward - and shooting days are not as plentiful as other options). I'm a regular at an outdoor range in WV, but it's currently undergoing refurb, so not a currently available option.

The NRA Range at the NRA HQ in Fairfax is crowded, but reasonable. There are a few ranges along or near the Rt 28 corridor (Manassas, I forget the name; Silver Eagle Group; Blue Ridge Arsenal).