As long as its the same back wheel, you should be able to use a freewheel remover, and then just use a cassette tool to put on your new cassette, or have your LBS do it. Attach your rear derailleur, cable, and shifter. Set your high and low limits, make sure your cable tension is right in all speeds, and it should be ready to ride! Make sure you have all the gears before taking it out for a ride.
Raleigh Mojave 8.0, Soul Cycles Dillinger 29er (project, to be a SS rigid), Kona Dew Plus
if it still has the splined rear wheel and is just using an adapter for the singlespeed .. you use the cassette tool (in most cases) to remove the adapter and drop a cassette in it's place ... if it has replaceable drop outs you may have to get a geared set if the other owner removed them ...