Duplex receptacles have (4) screws for termination points along with a green screw dedicated for ground. One side of the receptacle has (2) brass screws and the other side has (2) silver screws. The hot side of the circuit (black wire) should be wired to the brass screws while the neutral side of the circuit (white wire) should be wired to the silver screws.
You only need to connect to (1) screw on either side. If you look at the screws on one side you'll notice that a metal jumper connects the (2) screws together. This allows for both screws to be physically connected to each other so only (1) termination point is required.
Now in the diagram below, I have those jumpers labeled as J1 & J2. If you look closely you will notice that J1 has been split. This allows for a separate circuit to be wired to the other screw and allow the upper and lower receptacles to work independently of each other.
This circuit allows for the bottom receptacle to be switched while the top receptacle will remain hot at all times. To perform this circuit, you will need to use a 4-wire cable to allow for the extra circuit. 3-wire cable into the switch box and a 4-wire cable from the switch box the the outlet box.
The black wire (hot wire) coming in from the left is the source power. It is tied together with a wire going to the switch and the black wire going to the outlet. The red wire (switched hot wire) going to the outlet, wires into the other side of the switch and the white wires (neutral), tie together to complete the return side of the circuit.
One of the most common wiring configurations your going to find with outlets are shown in the diagram below. These outlets are not switched. They are connected straight from the power source and are hot at all times.
The diagram above shows (2) outlets wired in series and more outlets can be added to this circuit by wiring the 2nd outlet just like the 1st outlet to keep the circuit continuing on until you end the circuit at the last outlet. Now some electricians will use a (1)wire jumper from the outlet and wire nut together the circuits inside the box, but I prefer to use the screws on the outlet for a more secure connection. So if you are just replacing an outlet, I would recommend taking the wires off of the old outlet one at a time and putting that wire in the identical position on the new outlet.
The diagram below is the same as above but this circuit is switching the outlets.
The box for the 2nd outlet was removed from the diagram for simplicity reasons. The 1st box gets very crowded in this circumstance but I am sure you can still get the concept. The same goes here as the unswitched circuit earlier if you have or are adding additional outlets to this type of circuit.
Above diagram circuit shows power coming from the switch and the below diagram shows power coming in from the one outlet box.
View this video for a basic outlet change-out.