What style headlight are you using?
For a simple headlight system without the high/low beam option:
Battery Positive (+) post -->-- Fuse-->--2 wire switch-->--headlight.
The battery's negative (-) post would normally conect to the minibikes frame. The headlight would then pick up its ground source from its mounting location on the fork. (or you could run the battery's ground wire directly to the headlight bulb ground terminal if you prefer or is necessary)
Most motorcycle style headlights/automotive driving lights already have the bulbs ground terminal connected to the headlight buckets mounting bracket.
No regulator, capacitor or other devices would be used/needed for this very simple circuit. The wattage rating of your headlight would determine how fast your battery would run down and what amperage size fuse was needed. There's no danger of anything blowing up but the fuse would be there to blow in case your positive side wiring ever accidentally shorted to ground. (A short w/o a fuse instaled would cause the wiring to burn up)
Here's a pic of a type of fuse holder you could use/buy at most any auto parts store:
http://www.amazon.com/Bussmann-BP-HHD-Fuse-Holder/dp/B000BXKZMO
(I'd guess you'd want to run a 10 or meyby 15 amp fuse)
Theres lots of diferent style switches you could choose, but for this simple 1 wire headlight you'd just need it to have 2 wire connections and be rated for say a minimum of 10 amps. (the technical term for this type of
(on-off/2-wire) switch would be a "single pull single throw")
I'd probably use 14 gauge (or larger) sized wiring for this job.
If you dont understand any of this, just ask. Its really a simple easy wiring job but I probably made it sound complicated.