You are a funny one. Just for that, I will help you. First of all, you will need to pull your toilet, which is easy enough as long as the valve hasn't hardened over the years. Have a good set of channel locks or a wrench handy when you turn the valve off, hopefully it won't spray water out from the handle. If it does, put a soft crank on the nut around the valvestem to tighten the valve on the washer inside. Next, flush the toilet. Twice. Once to empty the bowl, then again to empty the bowl with what was in the tank. Use one of those annoying plastic cups you get at restaurants when your kids order a meal and scoop out the rest of the water that didn't flush. The toilet is held down, usually, by a nut on each side of the base, and the water line. Disconnect the water line from the toilet, (NOT THE VALVE). This connection should only be hand tight. Be careful, this whole toilet is only a fancy clay pot.
Pick up the toilet by putting your hands on the inside of the rim and picking it up where the center of balance keeps the thing from falling backwards. Have someplace handy to set it down but not on anything you care about because there is a wax ring underneath that probably has a little icky on it. Make sure you REPLACE THIS WAX RING when you do all of this part in reverse! I'M NOT KIDDING!
Next, if you aren't replacing your vanity, although you might consider this option at this point depending on how old things are, grab a flat shovel and start hacking away at the tile. Be careful not to hit anything you care about, and do the part near the walls and tub with a pry bar and a hammer. This part requires eye protection, and probably earplugs as well.
Keep working at it until you get down to the plywood subfloor. IF your tile person did their job right, there will be a concrete backerboard you have to take out first, but who knows what's under there. The point is, you want to get down to the sub floor.
Make sure your subfloor isn't rotting out from bathtub or toilet (remember that wax ring?) leaks, then install particle board in the room for the linoleum underlayment. Some people might suggest a cdx rated plywood, and this also works, provided you have a plywood smooth enough not to transfer the woodgrain through the linoleum surface.
All screws (screw the underlayment to the subfloor) must be absolutely flush with the surface of the wood, or again, you will transfer through the surface.
From here, there are several postings on the site regarding actual linoleum installation, and you can get advice from the flooring store you buy the flooring from. Don't skimp on your linoleum, buy the good stuff. You only want to do this once. Also, remember that the flooring adhesive will not come out of your clothes, so don't wear anything you care about when you do this. It's messy, and like eating pancakes, the maple syrup gets on everything.
Have fun, and search the board using ctrl-f then "linoleum" to find more posts.