Originally Posted by Halfraq9
Staying relaxed. In terms of drills, alot of slipping, rolling, ducking, etc. All this improves head movement and footwork. With alot of practice you'll see openings to counter.
Once you get the basics down, start sparring the lighter the better. Don't go hard or fast for awhile or you'll wreck your technique. Correct repetition is your friend at this point. Good Luck
Also, just a side comment. Counter-punching is essentially anticipation and effective utilization of an opening. It's about being able to read any telegraphing that comes before a strike and making the right call. You'll notice a lot of Muay Thai fighters watch for kick/knee telegraphing from the hips/legs during fights to setup a potential counter.
Another key item when it comes to countering is distance and range, learn how to effectively move in and out of range to dodge then counter. We used to drill that by using a long pole placed against the navel of two people training, a means of measuring the distance, and we would move in various directions (both toward and away, left and right) without dropping the pole. Our sensei had decided that the length of that pole was the optimal distance to maintain when not striking.