Fit the slip joint washer and nut over the end of the drain pipe on the bottom of the sink and slide it up about 3 inches. This washer and nut is included with your p-trap drain, available at any hardware store.
Place the longer end, which is the top end, of the p-trap over the sink drain pipe and thread the slip joint nut on the p-trap. Tighten this nut by hand and then with a wrench, moving the nut another quarter turn or so after it is sufficiently hand tightened.
Fit a reducing connector to any home drain pipes that are larger than 1 1/2 inches in diameter with another slip joint nut and washer. Tighten the connector by hand and with the wrench.
Connect a 90-degree fitting to the other end of the p-trap to the home's drain pipe by placing a slip joint washer and nut on the end of the fitting and attaching it to the p-trap. Tighten the connection by hand and the wrench again. If necessary, install a length of pipe to bridge any gaps between the p-trap and home drain line.