Step 1: Step One: Inspection
If things look normal, acquire a basin wrench. A basin wrench is a long tool that makes it easier to reach up to the fittings that hold a faucet to a sink. They are inexpensive and should be available at most places where faucets are sold. Additionally, an adjustable (Crescent) wrench may be needed.
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Step 2: Remove the Old Faucet
It may seem easier to get the new faucet first. However, many who are replacing a faucet for the first time find it easier to remove the old faucet first. This allows them to be able to bring the old faucet to the home supply store to get a replacement that is guaranteed to fit.
There should be two small pipes that descend from the faucet to the water pipes. They should be made of flexible plastic or a metal cloth covered tubing. There will be a nut on each end. The hot water pipe should be on the left and the cold on the right. If the connecting pipes are crossed, take the time to mark them H for hot and C for cold.
Using the basin wrench, loosen the nut for the cold water side and the hot water side at the faucet. If the connecting pipes look as if they need replaced, it is easier to just disconnect them at the shut off valve.
Once the connecting pipes have been disconnected, use the basin wrench to loosen the nuts up underneath the base of the sink that hold the faucet tight to the sink. Plastic nuts usually have tabs to remove them by hand. However, they are often too tight and need to be removed using the basin wrench. If there is a sprayer, it must be disconnected.
Step 3: Installing the New Faucet
Metal to metal threads should be wrapped with Teflon tape. Instructions often suggest to not use Teflon tape when plastic threads are connected to metal threads. Heed the written instructions that come with parts. Both Teflon tape and plumber's putty are inexpensive and should be available where you bought the new faucet.
Put things back in reverse order. Put the faucet down into the holes in the sink. Apply the nuts that hold it in place. Tighten them just a little. Check alignment of the faucet and then tighten them snug. Do not over tighten anything. Teflon tape should be applied to metal threads before you begin installation. Reconnect the connecting pipes. Tighten them tightly by hand, then snugly with a wrench. There is no need to bear down when tightening.
This is best done using a partner. Turn the water back on slowly while checking for leaks. If there are no damaged parts or crossed threads, things should be fine. If a small drop of water appears at connections, tighten them just a little. Barring damaged parts, there should be no leaks. Enjoy your new faucet!