My partner and I did ours about 18 months ago pre lockdown, but I think the procedure is basically the same. First thing to do is read and digest Jim's Guide on this site regarding changing your driving licence to the Spanish one, so you're fully briefed.
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What's involved? (All my remarks are qualified by the fact I don't know what if anything has changed due to Covid). First, you both need to get medical certificates in one of the specialised driver's medical centres around the country. We went to the one in Marques de Campo, Denia, the main shopping street in the town, it's between the small Santander branch and the Movistar shop, halfway down on the left going towards the sea. Look for the sign 'Centro Medico Conductores' sticking out from the wall. They are only open at certain times, the opening hours are posted on a notice outside. They are on the first floor. No appointment was required, you just rock up and wait your turn. Costs about 35 euros per person. If you are reasonably fit and healthy, it's something of a formality. Apart from the usual form filling, there's a dexterity/reflexes test run by the receptionist where you sit in front of a computer screen and use paddles like a 1980's computer game to move a cursor along a moving road. The idea is not to touch the road edges, you'll cause a beep every time you do.
Then you go in to see the doctor, who goes through your medical history, checks your blood pressure, checks your eyesight on a chart, shows you colour blindness diagrams. At the end of all that, you should be issued there and then with your certificates which basically say you're fit to drive. They last three months.
Then you need to make an online appointment at the nearest Trafico office to suit you. Yours, like us, is probably Alzira, which is more than halfway to Valencia. Resign yourself to a day out and time your appointment so you can treat yourself to a menu del dia afterwards! You'll need the application form filled out and printed off, plus other documents and your UK licences. See Jim's Guide. The office in central Alzira is fairly easy to find. There is some onstreet parking nearby. The public side of the office is typical, a waiting area with seats and a display board showing the appointment numbers. You need to check in at the machine when you first arrive, and get a ticket with your number on it. When you get called, as Jim says, go up to the desk, apologise for your poor/non existent Spanish and hand over the documents. I think you pay the fee there and then by banker's card.
They'll tell you they'll call you back by e-mail when they want you to return. What's happening is that they contact the DVLS in the UK for your details, so their reponse determines how fast things move. Eventually they'll e-mail you and tell you they want you to come back in, maybe three/four weeks later. You go back to Alzira again, same routine (I know, what a pain), they take away your UK licences and they'll give you a temporary licence (piece of paper). They tell you your Spanish licence will arrive in the post. Hopefully, it goes smoothly and a few weeks later, you'll be the proud owner of a Spanish licence.