I'm probably the worst guy to answer this, as I've never really been successful with it, but I think it goes like this: Take a larger syringe and bigger gauge needle and draw up the amount you need.
Then, yes, take, for example, an insulin syringe, pull out the plunger (obviously set it down someplace sterile, I use an alcohol prep pad), and shoot in your desired amount. Now comes the tricky part that I always screw up.
You put the plunger back in, but only slightly, so that you don't push out all of the oil you just put in, then you turn your syringe upward so that the oil runs down. If you've done it right, none of the oil should leak out from the barrel where the plunger is, and you can now safely push the plunger all the way in.
On a tangential note, and since we're hijacking, did you know that you can hold an amp upside down and no oil will leak out? This is useful if, when using amps, you want to save a needle and not dull the blade by pressing it against the glass. You can just pull everything out of the top of the amp