Well, basically you contact your front- and back contact and measure the current while applying a voltage. This can be done in dark and illuminated, preferably by using a solar simulator that nicely reproduces the spectrum of the sun. There are many different ways possible. To prevent the influence of contact resistance, you can do it in a 4-point probe geometry. You can use concentrated illumination, and so on.
For a basic I-V characterization you just need to measure the current between let's say -2V to 2V in dark and illuminated. To get reliable (and comparable) results you need a calibrated solar simulator.