My house is little dated and the faucet started leaking in the bathroom, so I decided to replace both of my bathrooms' faucets. (That is why my pictures are a mix of two different sinks.) If you need help removing your old faucet you can check out Removing a Sink and Vanity here on instrucables.
Step 1: Pieces
To begin, unpack the new faucet and be careful not to lose any of the small parts.
Step 2: Preperation
Now, attach the two hoses to the water supply valves in the wall under the sink. This usually requires a crescent wrench and some plumbers tape. To apply the tape, wrap 1 to 2 layers around the threads before tightening. Plumbers tape isn't an adhesive as many people might think, its really more of a thin plastic that helps make a water tight seal.
Don't turn on the valves yet or else you will get very wet, and so will the rest of the room.
Step 3: Attaching the Faucet
The first part of the faucet that needs to be installed is the plastic piece that goes between the sink and the faucet itself. After that, simply set the faucet in.
There will be two nuts, most likely plastic, that can be tightened on the underside of the faucet to hold it down with a crescent wrench.
Step 4: The Drain
This is the most complicated part of the proceedings.
With waterproof bathroom caulk, coat the underside of the drain opening and set it down into the bottom hole in the sink. (Images 2 and 3).
Before the caulk sets, on the underside of the newly placed drain place rubber washer, plastic washer, and plastic nut. Tighten to hold the drain in place.
Screw on the next piece of drain. It will have an arm that will be needed in a moment.
This part is very hard to explain, and there are many little pieces. The faucet instructions should at minimum have a diagram to help you figure it out. I shall try to explain as best I can. From the top of the sink, drop in the thin metal part that will control whether or not the drain is open or closed. Next, take the plastic nut off the arm of the second drain piece and the put it back on with the white sphere with the metal arm in it. Now, attach both the metal control arm from the top and the metal arm attached to the sphere to the long flat metal piece with holes in it. The holes allow you to adjust for the size and shape of the sink and drain.
The next part is a true puzzle that may require many trips to the hardware store to find the proper curves that will allow you to connect the drain from the sink to the drain in the wall. Once you do find the proper combinations of shapes, be sure to tighten all joints securely to prevent leaks.
Step 5: Connecting the Water
This is a fairly simple step. Tighten the nuts at the end of the hoses to the threaded pipes at the underside of the faucet. It might be wise to wrap some plumbers tape on the threads before tightening, but be careful not to put to much tape or wrinkled tape because this will break the seal and it will leak. Now, you can turn the valves on.
Step 6: Finish
Assuming nothing leaks, you're now finished!