Start out by doing all underhand swings, and getting used to the shuttlecock (also known as a birdie).
Once you've gotten a feel of the weight, of both the birdie and the racket, and can gauge the distance of your underhanded shot..
Try to aim for specific positions. Make sure to notice the angle of your racket.
Never have it completely flat. Try to angle it a bit like 10-15 degree's when your racket is making contact with the birdie.
Once you've gotten a hang of getting the birdie over the net, and can relatively aim it where you want to go, start focusing on how you grip the racket.
You should never use 2 hands. Always use one hand.
You'll get more control over the racket at first, by placing your hand closer to the shaft, instead of the end of the handle.
Place 1 or 2 fingers on the shaft for extra support, and use your wrist in a 'snapping' motion to hit the birdie.
You'll find the snapping motion hard at first, and that's to be expected.
Remember at this point you should still only be under handing the birdie.
Don't try to win with a power smash/spike while your learning how to play.
Outlasting your opponent, by simply keeping the birdie in the field, and knowing how far/fast/high/slow you can hit the birdie to get over the net, is a must.
Now, once you've gotten your wrist 'snapping' a little figured out, you can start hitting the birdie sideways.
When hitting the birdie from the side, you'll want to aim for the centre of the court to start.
The angle your aiming for is still 10-15 degree's.
You want your birdie skimming the net by about 1-3 inches.
Side 'snapping' is harder, and you'll want to extend your wrist farther and faster.
You'll feel like your wrist is in molasses for a long while compared to your underhand swing.
Again, this is expected.
After about a week of underhand and side swinging, start throwing 'highball' with overhead swings.
Don't even try to hit it straight.
Your goal is to hit it high and far from the net, but still in bounds.
Again, always using your wrist.
Now, with all this wrist snapping exercise out of the way, you'll be able to start 'smashing' the birdie.
Smashing the birdie is a combination of your arm + wrist.
Remember, your wrist is more important then your arm strength.
Generally, imagine your arm as being a floppy whip.
When you use a whip, you extend the rope as far as possible then 'snap' the end.
So the same thing with your arm.
Extend the arm as far as possible, like a limp noodle almost, then when your arm is coming forward, snap the wrist as fast as possible.
Your goal is to hit the birdie at the top of your reach, in the middle of the racket, with the angle being (-)10 to (-)15 degrees.
If your closer to the net, and your wanting to 'spike' your shot, your looking for a 30-45 degree angle.
Once you've got all that mastered, you'll want to figure out backhanding the birdie, (again with the wrist.) works.
It's relatively easy, just a little different.
tl : dr Use your wrist instead of your arm to whack the shuttlecock.
Note: I'm not a professional badminton player by any means, however when I did play in highschool,
I was one of the best players (top 4 for sure.. and we only played like once or twice a week)
I also got to play against college players in a mock tournament and beat 2 out of their 5 players.