Each district is different.
In the New River Valley, there are two avenues to receive the vaccine:
Through the local health department. Registration starts at https://vaccinate.virginia.gov and as long as your address is within the NRV, phase 1b and 1c will get a call or email in 1-2 weeks, sometimes just a few days. If you’ve been registered for a while, go update (there are some new questions) and re-submit your registration.
Through pharmacies. Finding a slot starts at https://vaccinefinder.org, but I would also directly call any local non-chain pharmacies near you. Just recently, Blacksburg Pharmacy was offering shots to patrons of the nearby Food Lion on their walk back to their car.
About 20% of the NRV’s population has been administered at least one shot through #1 and about 5% through #2, though option #2’s availability is newer and has really exploded in the last week or so.