Changing a Signal's DC Offset
Capacitive coupling has been suggested, but this has two big disadvantages:  


Your signal is no longer a square wave  
It will only center your signal around 0V if the duty cycle is 50%; you'll see the signal go up and down if you play with the duty cycle


A good function generator will have a potmeter to set an offset to the signal. One way to do this yourself is to make a resistive voltage adder. Connect signal and offset voltage each via a resistor to an adding point. Very simple, but this will change the signal's output impedance. A better way is to do this actively:  



Here signal and offset each see only the input resistance to the virtual ground, so that their resp. levels don't influence each other. The opamp will give it a low output impedance. You may want a fast opamp (high Gain Bandwidth Product, GBP or GBW) depending on the square wave's frequency.
Also keep in mind that this inverts your signal.