The forehand low serve is more complicated than the backhand, because it involves some body movement and dropping the shuttlecock.
Stance, grip, and holding the shuttlecock
Stand with your body turned somewhat sideways-on to the net, with your left foot in front and pointing forwards. Your right foot should be farther back and (comfortably) turned out to the side.
Your weight should be mostly on your back foot.
Hold the shuttlecock with all your fingers gently cradled around it. For a forehand serve you must drop the shuttlecock into the path of the racket; this is different from a backhand serve, where you
hit from the hand.
Weight transfer and body turn
Before you hit the shuttlecock, you should begin a smooth transfer of weight from your back foot towards your front foot. The hitting action takes place during this body movement.
During this body movement, your chest turns to face the net. You may lift your back foot partly off the floor and swivel on it, but the service laws require you to keep some part of both feet in contact with the floor until you hit the shuttlecock. You must not lift a foot entirely off the ground, and you must not drag a foot along the floor.
As you turn your body, bring your badminton racket forwards with your elbow held in close to your side. Your wrist should be cocked back fully (hyperextended), and your forearm should turn outwards (supinate) so that your palm is facing upwards somewhat.
Drop the shuttlecock into the path of your racket, in front of your body. For accuracy, delay the drop so that the shuttlecock only falls a short distance.
Keep your wrist bent back and gently push the shuttlecock over the net. Follow through smoothly (don’t stop or rebound after hitting) and allow your wrist and arm to return to neutral.
The racket movement should be mainly forwards, not upwards. This helps you make a flatter serve.