Post a picture. An overview, and inside each of the sink sections, showing the plumbing.

We just removed an old wet bar. Its was old and flimsy but I did hire a plumber to unhook the water lines and pea trap thing. At that time he replaced the hot and cold water valves which is important in old houses (crappy). He left off the handles so it would be easier to slide the cabinet out, we did have a slim saw to enlarge the hole some so the valves would clear it.
Basically unscrew every screw you see and dismantle it.
Not hard.

You have to undo all the plumbing first. And it will leak, even if you have shut off valves. If the mirror rests on the splash, it has to come off first. But usually the light fixture is in the way for that, so it has to come off first and you use work lights. This isn’t a big job. But it is a big job if you don’t have the right tools and experience. If you don’t have enough levels, understand fillers, and know how to shim properly, take a couple of weeks and learn, or hire a pro.

Pipes, pipes, pipes! I replaced a two-sink vanity that sat on the floor with a two-sink wall-hung vanity. The new vanity was divided into three sections with drawers in the middle. A couple of the cold and hot pipes had to be moved so they'd be within the sink sections. I had to cut the wood at the back of the vanity to allow the drain pipes to pass from the sink sections to the center drawer section (there was room as the drawers were shallower than the vanity) where the drain pipes were.

Drywall? The old vanity top was pretty low. I mounted the new vanity higher (36") and it covered up the damaged drywall.

Here are a couple pics of the vanity in question...

there's also one of those ol 90's hot tubs that would have to go as well. I wouldn't want to do only one side..

The cultured marble might look nice in these pics, and is very usable, but there are many marks of discoloration (orange color) from previous tenants likely putting iron on counter.

The first thing is to determine where the home’s shut off valves are. That’s inside the dwelling, and outside at the street or meter. If there are shut offs under those sinks, they likely are frozen open and will self destruct when you try to use them.

Next, figure out what type of plumbing supply lines that you have. CPVC? Copper? What material supplies are you going to need? Go to the store and get some stock fittings, glue, solder, etc. You'll need all of that now and for future projects.

Next, Shut if the water to the home, at the main shut off, and drain the internal pipes by opening the most downstream one to drain. Cut off the shut off valve and glue or sweat a cap to them. If you haven’t sweated copper bis fire, practice that for a week or so before tackling this. Any water in the lines will make this really difficult. Leave the pipes long enough to be able to extend with new pipe or a new valve. Cut the drain waste arm going into the wall. And stuff a rag in it. Trim up all the spaghetti hanging down from the top for easier handling.

Once the pipes are capped, then cut free the caulking holding the top to the walls and vanity. A long slim blade, and then a cat’s paw pry bar will be needed. Then a bigger pry bar. These things are much heavier than you think they are. You will need help to lift it up and off.

Once the top is off, then find all the screws holding the vanity to the wall, and remove them. Look for screw at the bottom too, holding shims there. You and your helper tilt it forward to be sure you haven’t missed a screw. Then slide out the bottom. You likely will have some wall damage to repair.

You can put it on Craigslist to sell it or donate it if you don’t damage it or the top. If you damage it, use a sawzall to cut it up into manageable chunks to dispose of. Many municipal waste companies don’t like construction debris in the household cans. If that’s the case here, you’ll have to haul it to your local dump. Some will require a dump fee. Some allow so many free trips per year. Use that opportunity to get rid of a few more things in either case.

Putting in a new vanity, top, and plumbing, is more than twice as hard as demolishing the old. It’s an advanced DIY skill. You need to own multiple levels, and know how to shim things to level in all 6 directions. Then you screw it to the walls through the shims. Install the faucet to the top first, before setting. Shim the top level, and silicone to set. Then you redo all of the plumbing.

I’d suggest making friends with your new neighbors and find a friend with some DIY skills that you can help with her jobs a time or two before tackling this. You will need tools. Those tools will cost as much as hiring a pro to do it for you. But you get to keep the tools to do it again! Good luck!

Based on the recent installation of three vanities and four sinks:

• If the under-sink valves can be turned off, don't mess with the pipes until you've removed the vanity. It's a lot easier to work with the pipes absent the vanities.
• Install the faucets after you've installed the countertop if you'll be using silicon between it and the walls. If the faucets are in place, they'll block the tip of the silicon tube, preventing you from making a clean line of caulk. I made the mistake of installing the faucets first.

A counterpoint. :-) With full back vanities with just access holes, you can’t even really remove the vanities with the shut off‘s in place. Or install new ones. That’s why contractors get all of the impediments out of the way and just cap the pipes.

I‘m not sure why you’d have issues caulking between a vanity top and the walls with a faucet in place, unless the faucet holes were too close to the wall. That can be an issue with prefab tops, but the cure is to place the caulking at the wall before you install the top. Then clean up any squeeze out.

Installing the faucet to the top before install is SO much easier than buying a basin wrench and laying on your back trying to maneuver anything between the tiny space between the bowl and the wall. That’s for the birds!

1. Neither the old nor new vanities had a full back.
2. The faucets were close to the wall.
3. I couldn't caulk the wall first though it seems like a good idea. I had to first put backer rod between the countertop and the wall because the wall was imperfect and then apply the silicon.
4. Attaching the faucet to the countertop before installing it is easier.

If you have to ask.... call a pro.