You'll find that the hair on the underarm of a guy is usually very long and straight. Grab it into a bunch with one hand like a pony tail and cut most of the length off in one go with a pair of scissors.
Cleanse, dry, apply oil or talc (talc if it's a hot day) and separate the hair into the different directions.
You'll find that on men that strip wax has a better result than hot wax because the hair is less coarse than on a woman but that's because we're always removing it in one way or another whereas guy's tend to leave it alone.
Whichever wax you decided to use really S T R E T C H the skin taut and rip the stip or wax off very quickly for the most painless results. If you do decide to use strip wax, remove once and then fold the loaded end of the strip down so that end becomes your handle.......that way you're only applying a clean end of the strip to the skin. Then get a new strip. A wax strip loaded with wax will pull and tug at the skin and cause bruising and soreness.
If you're wondering why I'm not telling you to only use hot wax it's because having waxed countless people, I know that every now and then you have to change the rules to do what's best for your client.