Replacing a faucet starts with removing the old faucet. Occasionally, this can be a real chore.
Typically you are laying on your back trying to feel your way up to the underside of the faucet to get a wrench on the nuts. The nuts hold the faucet to the sink, and so these must be removed before you can install the new one. Turn the water off first, and then remove the water supply lines that lead to the faucet. You will get a little water that dribbles out.
If you can\’92t get to the nuts with a standard wrench, try using a basin wrench, with has jaws and an extension that allow you to get to tight places. This may be enough to get the nuts to loosen. There are times though that it seems nothing will work. For these times, you may need to break out a saw.
A hacksaw blade will cut through the nuts, but it will take time. Chuck a blade into a close-tolerance handle and start cutting (you may also try a nut-splitter tool, but much of this depends on how much space you have there). The close quarters really is the issue. If it was a wide open space, you could use any tool you had and be able to place leverage on it to remove it. I remember having to use a reciprocating saw on one faucet. I had to cut it into a few pieces before I could get it out. You may need to get creative.