exfoliate your underarms frequently to peel away the dead skin. You can always use a pumice stone to exfoliate those dead cells. If you're using deodorants, avoid alcohol-based ones.

If you often shave, switch to waxing instead. It's painful at first but you'll get use to it. You'll notice some minor bleeding (petechiae) but don't worry coz it's temporary.

after waxing/plucking, apply some baby oil or simply use the oil wipes available inside the wax strips package. DON'T PUT ANY OTHER REMEDIES as they work as irritants. you wont want your underarm get burned!

other than that, you can use NATURAL YOGURT and spread evenly a think layer on the dark areas. Leave it for at least 20mins. Rinse with water. Repeat this method every week and you'll notice some changes.

You can mix the yogurt with a zest of lemon and apply the mixture on to the dark areas as mentioned above. Both lemon and yogurt work as best natural bleachers and exfoliants.

p.s: Do bare in mind that the last two methods will only show results if you do it often.
All the best!!!