I discovered this trick some time ago, but it's not the kind of thing that fits anywhere in casual conversation, and so I was doomed to be fresh and odourless alone.
This is one of those bathroom secrets that nobody speaks of but is certainly known (for other examples, see throwing toilet paper in the bowl when taking a dump to stop the water splashing on your ass). There's certainly no pleasant way to pass this idea from one person to another among civilised folk, but by the power of the internet, all is revealed!
1. Armpit hair is hair too. Grab some shampoo.
2. At the sink, wet your hands and use this to wet your armpits.
3. Rub the shampoo on your 'pits.
4. Leave it for a few minutes and wash your hands.
5. Once the shampoo has soaked in properly, start wetting your hands and washing the shampoo off.
6. When you think you're done, dry your armpits with a towel.
7. You're not done. Repeat from step 5 until you get absolutely no shampoo on your hands when you rub your armpits. The idea behind this is that the shampoo retains the smell and so it has to be completely washed off.
8. wash your hands (which will smell like your armpits did!)
And now you know. Armpits armpits armpits!