Line up all of the tools you need as well as the sink and its various parts in one area. This will allow you to get to what you need easily.
Mark a spot on the wall with a pencil to indicate exactly where you want the sink to be. Then, place the bracket used for mounting the sink, which is usually included in the box, at the desired position on the wall. Use the torpedo level to get the most accurate positioning of the holes and mark the spot for your holes with a pencil. Next, using a power drill and screws, mount the bracket to the wall.
Attach the faucet to the sink and connect the water supply hoses to the faucet using the channel locks and crescent wrench. Don't put those channel locks down just yet because you will also need to use them to connect the drain and tail piece to the sink.
Apply plumber's putty to the drain flange lip before placing it through the hole of the sink. The drain flange lip is the silver part of the drain in your sink --- the part that your sink stopper sits in. Applying the putty around this area ensures that water won't seep through the drain and cause water damage.
Hang the sink on the bracket to mount it onto the wall. Place the torpedo level on the front lip of the sink to make sure that the sink is level.
Connect the water supply hoses to the water supply stop handles on the wall using the crescent wrench. Do not turn the water supply handles on until the drain has been connected.
Connect the p-trap, which is the u-shaped pipe located under your sink, to the tail piece coming from the drain. If the tail piece is not long enough, use an extension piece to reach the p-trap. You may have to cut off some of the extension piece in order to adjust the proper length.
Open a tube of caulk and place the tube into the caulking gun. Apply a bead of caulk around the edges of the sink that are flush against the wall. Press the caulk into the groves by running your index finger along the applied area. Use a wet rag or moist sponge to remove any excess caulking from the wall and sink.