Sure. Think about it as being water: you have a big lake/reservoir that empties when the engine starts. What you want to do is make a second reservoir (tank) that you fill when water is plentiful (i.e. engine not cranking), and put a one-way valve in it so it won't run back into the lake when it's dry. Maybe that analogy helps
So basically you connect your battery to the power supply through a diode (a checkvalve for electricity) so current only flows to the power supply. Then, you need an 'electricity storage' betwene the diode and the power supply for when the main battery isn't enough (cranking). The storage can be another battery (much smaller; little sealed lead-acid or gel cell etc...) or a lot of capacitance (like car audio caps).
[battery+]--------|diode>----[+ side of cap]----- PSU +
Then ground the - of the CAP and PSU.
So power goes from battery through diode and fills cap while powering PSU. When battery voltage drops, the diode stops your cap from draining back to the starter-motor, and all the cap's power is left for the PSU.