Easiest way to make printing head spray ink?
A lot of that is proprietary but I've spent a lot of time reverse engineering print heads and building printers :)   Usually the firing voltage is high in the 24/30 V range.   If you just want it to spit you can usually drive some current through it at the appropriate voltage and get some ink to come out (I assume you have a resistive head and not a piezo most heads now a days are resistive).   I'd start by trying to just pulse some through it as you don't want to hook it up continuously and burn out the head.

Your just looking to get a short burst, heat up the tiny element behind the nozzle and get the ink to fire out.    

Whose head are you using?

Actually Printing

To actually print something takes more effort, we developed dedicated silicon just to do that.   But basically you convert the pixels or dots you want to print into high voltage firing pulses that activate each nozzle.  So usually the first step after spitting a blog of ink onto a page is to print out some test pattern by firing multiple nozzles.   You'll notice that there are a lot more nozzles than there are pins though :)  So to figure out the right sequence you'll need a scope or better yet a logic analyzer.

Printing and moving across a page or object?   That's a whole different story that will involve some encoders and control loops :)