Compress the fuel in a small area and then apply some high voltage. It’s probably not much different than a spark plug in a car.

They actually injected triethylborane to act as a match and initiate combustion (TEB auto-ignites at freezing temperatures and burns ridiculously hot).

The plane had a limited number of TEB "shots" and those were needed after each afterburner use, or when restarting the engine in mid-air (as crew needed to do under some conditions), so they had to be carefully managed.