There are two things I found key to succeed in crits. The first is to stay out of the wind and save your energy but still cover the front and be ready to close a gap. The further in front you are the more energy you burn, the farther back the less you can cover a break and the more energy you waste braking in corners and dealing with the yo-yo effect.
The second is to figure out which kind of sprinter you are. There is the short fast accelerator, Cavendish being the classic example. You wait till the last second and accelerate through and grab it at the line. The second is the long sprinter. You go early and build a big gap. On a 1 mile course, you'd go with 2 laps or more to go. And the last is between these 2, you'd attack soon after the last lap started, accelerate hard, build a gap, use your faster cornering and leave enough to accelerate and hold off the final sprint.
Staying on your line is what keeps everyone safe. You need to be going through the turn with the same trajectory as everyone else. When you brake in a corner the bike stops turning and goes straight, and if there are 10-20 of you going through it can be calamity. This is as dangerous as it gets and people take it very personally and seriously. The inside line is shorter and quicker but it's more crowded, the outside is slower but usually not as packed. The lamo move is to start on the outside and then dive the corner. DO NOT DO THIS. Bike crashes are nasty, nasty business. We all have jobs and families to go home to.