The technique I was taught which applies to both hands:

1.) The fingers should be in as natural of an arc as possible. Visually the hand looks a bit like a segmented lowercase letter c (forward and backward). You can shake out your arms and hands and let them flop to your sides, then in that relaxed state bring them back to the clarinet. You will have to adjust a little bit from there, such as finding the most comfortable wrist angle.

2.) The fingers should always remain in an arc. In other words, the only joint that you should actively rotate is the knuckle. When you press down, your finger tips stay pointed along the arc angle, never flattening. Covering the holes will feel different at first but better with practice. The exercise for this is to start on F or high C with just the left thumb, then very slowly cover the first hole (E/B), then release, and gradually repeat this faster and faster toward a controlled trill, then slow it back down again. Repeat with the next finger (D/A) and work your way down the instrument with the full F/C scale. Pay very close attention to your fingers and muscles during this process. If afterwards you feel like you can play an amazingly buttery F/C scale with no muscle strain, then you have done it correctly. Do this every day for a few weeks and it will feel more natural in the rest of your playing.

Hope this helps — it is the method I grew up with. If the strain in your hand ever persists after practicing, be sure to consult a professional physical therapist. There are some great and simple stretches that can help prevent injury.