Installing a sink isn't as difficult as it seems. You'll need to make sure you make a template and measure the area under the sink to make sure it fits correctly. If you're also changing your cabinet or vanity you'll have to measure these areas as well.
Most manufacturers provide a template that you can use to draw the opening of your sink. You'll want to center the template on the sink cabinet at least 1½ inches back from the front edge of the counter. After you tape the template down, draw the outline with a marker. After you remove the template you'll drill around the outline to cut out the hole. You can use a saber saw to do this. Then install the faucet before you put in the sink.
Apply silicone caulk underneath the lip of the sink to create a watertight seal. Flip the sink over and place it into the hole. Based upon the instructions for installing your sink you may have to use mounting clips that attach under the sink's lip. When you tighten these clips with a screwdriver some of the caulk may squeeze out so be sure to wipe it up with a rag.
Once your kitchen sink is in place you'll need to connect the faucet lines to the hot and cold supply lines and the strainer to the waste line. Turn on the shut-off valves and let the water run through the faucet without the aerator. Run the water for about a minute then replace the aerator.