I exercise every evening:
This is fine.
I do exercise every evening:
You need a determiner after "do" for this to make sense. For example:
- I do some exercise ...
- I do a lot of exercise ...
- I do a bit of exercise ...
As Dori said you can use it as a response to an accusation as well:
A: You never exercise.
B: I do exercise! Every evening in fact.
You do see "take" used, but it's not that common (here in the UK at least). It sounds a bit weird to me, personally. It also needs a determiner.
- I need to take some exercise.
"Get" is more commonly used. I don't agree with Dori that it suggests different types of exercise. It could be the same thing (always running, for example), but it doesn't specify what that thing is.
- I need to get some exercise.
- I need to get a lot more exercise.
You can also simply say:
- I need to exercise.
You always use it in singular form, in this case. Even if there are different types:
- Pushups, sit-ups and running are three different types of exercise.
Exercises is used to talk about drills, or practice routines:
- Complete the following exercises as part of your English homework.
- The military completed a range of naval exercises.