Starting with the underside, since you are switching to a single bowl some of your fittings will not line up anymore, or they might be cut too short, so you might want to start with a new kit. You might find all of this in one kit, but often you need to buy additional extensions., etc.
If the sink doesn't come with one you'll need a basket strainer, this is the part you apply putty to the underside of the strainer and put the washers on the underside of the sink and then tighten the big nut while holding the strainer from moving. Make sure the putty isn't cold and hard, room temperature and soft is what you want. Roll it into long strings and pack it around the strainer, excess will squeeze out. You can install this before you install the sink or after. If I'm working by myself I do it before as it's hard to tighten the nut underneath while holding a big screwdriver in the top of the strainer from above.
The tailpiece attaches to the bottom of the strainer, you can get a long one with a dishwasher attachment.
Next is the p trap, then the waste arm which terminates in the wall, or in your case, the glued fitting that drops down into the floor. You'll need to cut these as needed to fit your application, but be careful not to cut them too short.
Pay attention because some of these pieces use different washers.
I think the white plastic is easier to install than chrome, but watch it closely for 2-3 days after because sometimes a leak will show up late. I don't use any flex pipe because I don't think it works as well.
Now to the top. Your existing ss sink is held down by little screw clamps on the underside that put pressure against the bottom of the countertop material, so remove them and pay attention to where they where and how they work. I like a headlamp to keep your hands free, and you have to be a contortionist laying on your back under there so clean everything out first.
There should also be some type of sealant between the bottom of the sink flange and the top of the countertop and this can be a pita to break free without damaging the countertop. Most likely it will be clear silicone. Use a combination of a sharp utility knife and a thin pry bar to coax it up, carefully. Put thin wood or equivalent material under the fulcrum of the pry bar as needed to protect the countertop.
Now the most important part, last. The cutout for your new sink needs to be the same size (or slightly larger) as your existing sink. The new sink will come with a paper pattern that you cut out and place on the countertop and trace the cut lines onto the countertop. Obviously you have a big hole in the counter already so ideally the cut out is exactly the same size, but it may not be. You should be able to tell if it's going to work before you start by measuring the dimensions across the top flanges of both sinks.
If you have to cut the countertop use a jigsaw and put blue tape on the countertop then trace your cut lines on the blue tape.
Hopefully you don't have to cut the countertop. When it comes to the install of the sink, I like the small squeeze tubes of sealant vs a caulking gun size.
