This can be simple task IF the circuit goes to the outlet box first and then to the switch. You will need to remove the coverplate and receptacle very carefully. Initially you can turn off the circuit breaker to the outlet so you can safely pull the receptacle out and look at the wires entering the box. If you find a single set of conductors entering the box (black, white, and ground) the power source enters the switch before running to the receptacle. If you find two sets of conductors in the receptacle box, you should find them tapped together, possibly with the white going to the switch being tapped to the black wires or connected to the receptacle (this would mean two white wires connected with one having a piece of black tape on it.) Many contractors do this (though not 100% code compliant), to carry power to the switch on one of the two conductors and bring the switched power conductor back to the device being controlled.
If two sets enter the box - If conductors are tapped together in the box, remove the wire nuts and connect a piece of wire about 7" long to the black and white groups and replace the wire nuts. Look at your receptacle and you should see a thin flat copper strip with a small bent tab sticking up between the screw on each side of the receptacle. Take a pair of pliers and break the strip and remove the piece completely that breaks free. You then attach the two 7" leads under one screw on each side of the receptacle and attach the two wires from the switch to the other two. This is called split wiring a receptacle.
If power enters the switch box first you will need a length of 4-wire conductor (red, black, white, ground) to replace the wire from the switch to the receptacle box. The rest is about the same in regards to breaking the copper strip, but you will need two 7" pieces of white insulated wire to tap together and connect to the screws on the same side of the receptacle. The red connects under one screw on the other side and the black under the other.
If two sets enter the box - If conductors are tapped together in the box, remove the wire nuts and connect a piece of wire about 7" long to the black and white groups and replace the wire nuts. Look at your receptacle and you should see a thin flat copper strip with a small bent tab sticking up between the screw on each side of the receptacle. Take a pair of pliers and break the strip and remove the piece completely that breaks free. You then attach the two 7" leads under one screw on each side of the receptacle and attach the two wires from the switch to the other two. This is called split wiring a receptacle.
If power enters the switch box first you will need a length of 4-wire conductor (red, black, white, ground) to replace the wire from the switch to the receptacle box. The rest is about the same in regards to breaking the copper strip, but you will need two 7" pieces of white insulated wire to tap together and connect to the screws on the same side of the receptacle. The red connects under one screw on the other side and the black under the other.