How to make a phase shifter?
It depends heavily on the frequency at which you want to use your phase array antenna how you would implement the phase shifting. Possible solutions are:


separate receivers/transmitters per antenna or set of antennas, this phase shift can be implemented in baseband or at the LO signal
a shorter or longer transmission line to the antennas
RC filters and/or polyphase filters
some form of delay line


Note that usually a phase array antenna is used for a certain narrow band so the phase shift only has to be predictable at that particular frequency band. So in practice the phase shift is simply a time delay of the signal.

There might be more that I can't think of now.