One tip up front. Do not try to think about two stroke improvement or maintenance things at one time. Pick one thing to check or work on, work on it for a short while, then move on to something else, then come back to that thought and check it again. Trying to think about two things at once usually results in neither one being improved, and thinking about one thing too long can lead to over-analysis and boredom!
Flex Your Wrist
When your hand goes into he water (the entry), you have to move it from the entry into the catch position. The first step to get into the catch is to tip the fingers down slightly by flexing the wrist. Starting from when the hand enters the water, you extend your arm forward, pointing your fingertips toward your destination. When your arm is fully or almost fully extended, you need to move into the catch position.
To get to the catch, start with a slight wrist flex to tip the fingers down, then follow that with elbow flex, tipping the forearm down, leading into the catch or early vertical forearm position. By flexing your wrist, you lead into a good catch position. A good catch puts your fingertips pointing down and your elbow pointing up. A line drawn from your fingertips, up your arm to your elbow would be at 90-degrees from your direction of travel - your fingertips are pointing down at the bottom of the pool.
Breathe on Both Sides
If you are swimming more than 10-20 meters or yards at a time, you probably need to turn your head to breathe, unless you are using a snorkel. When you swim, you should keep your head aligned with your body; your head should also stay aligned when you turn it to the side to breathe (one way to work on this skill is to use head point drill). When you do take a breath, you will probably like to breathe to one side of your body more than the other. You will like either breathing right or breathing left more than the other. If you can get over this, and become equally at ease - or almost so - to breathing on either side, you will have a more balanced stroke.
The only way to get better at breathing to both sides is and practice. You might use alternate breathing technique, by taking one breath to the right side, then taking your next breath to the left, and continue to alternate breathing sides with each breath.
Another method, that I favor, is to only breathe to one side, but to alternate that side every length of the pool. This works for me because I do a lot of swimming in outdoor pools, and I like to breathe away from the sun. I will swim 25 meters breathing to my left, then turn, and breathe to my right for the next 25 meters. I will always breathe toward the same side of the pool. This works well for open water swims, too, when it allows you to breathe away from the waves.
Alternate breathing also helps in race situations as it allows you to see more of the pool and your competition. It can also allow you to spot some landmarks in open water races depending upon how the course is set up.
Try thinking about these - or other stroke improvement tips - during parts of your next workout.