"Understanding is rock. Memory is sand. Build on rock." -- Edward Burger and Michael Starbird, The Heart of Mathematics.

Here are my suggestions for doing math homework.
Note that there is some element of order here.

Overall Strategy

Read the relevant section of the textbook before going to the class where it will be discussed.
Try to understand the material, but don't be too worried if you can't.
If you have time, try some problems.
Go to the class. (Didn't expect that one, did you?)
Since you already read the text, this won't be the first time you see the material and it will make more sense.
Plus, if everything's not crystalline in your mind, you'll have questions. This is the perfect time to ask them.
If you don't read ahead, you probably won't recognize which things do and don't really make sense to you.
Before the next class, try the assigned problems, regardless of whether they're explicitly part of your grade.
You don't learn math by watching, you learn it by doing.

Reading

There are all sorts of things to keep in mind when reading a textbook. Those apply here.
The main thing I'll add is this:

When you get to an example, try to figure it out before reading the solution.
If you get stuck, go ahead and read what they've written for a hint.
Stop reading when you get to the first thing that you didn't do in your attempt.
Make sure you understand the step you didn't think of before.
(How does it work and why is it appropriate?)
Try to continue from there on you own.
Repeat if necessary.

Doing Problems

This is important.
The biggest mistake I've seen math students make is to attack each problem by looking for an appropriate example to mimic.
The second biggest mistake is checking your answer immediately in the back of the book and trying to reverse-engineer the procedure.
Your primary evaluation is on exams, where you don't have examples or the back of the book to help you.
Don't practice with a crutch when you're tested without one.

Don't check the back of the book immediately after each problem.
Either try all of the problems before checking or at least do them in chunks.
Bang your head for a while against problems you don't immediately know how to do.
Think through what you know about the ideas involved and look through your bag of tricks for something that might be useful.
When you're tired of banging your head against a particular problem, don't stop working; just move on to another problem.
When you've banged your head against all the problems you can stand, make notes about what things were causing you trouble.
Now go back and reread the section, with your trouble points in mind.
Watch out for things that might help, and make notes of them.
When you're done rereading the section or you've got new ideas for all of your trouble spots, go back and retry the problems you didn't get before.
On those problems, don't just pick up where you left off; start over.
The main point is to prepare like you'll be evaluated.
e.g. If you don't get to use notes on an exam, don't use them when you're doing homework.

Preparing for Exams

Many people feel like they know how to do everything at home, but they freeze on exams.
If you're not following these study tips, test anxiety probably isn't your only problem.
If, however, you are already studying properly, here's a 12-step program that might help you for exams.

Go through the sections, including the reviews, and pick a problem or two from each.
Pick odd numbered problems so you can check your answers later.
If possible, pick problems you haven't already done.
Make sure you're not just picking the easy problems in each section.
In random order, copy the problem statements onto a sheet of paper.
This is your sample exam.
Set a goal.
Aim for 70%, 80%, 90%, whatever.
Set up a reward.
If you reach the goal, you win the reward.
Make it something you really want to do, like eating an ice cream sundae.
If it's something you wouldn't normally do, so much the better.
Set up a punishment.
If you don't reach the goal, you get the punishment.
Make it something you really don't want to do, like scrubbing your neighbors' toilets.
Again, something you don't normally do is best.
Put away your books, your notes, your calculator, and anything else you won't actually get to use when you take the real exam.
Sit down at an uncomfortable desk.
Give yourself a fixed time.
Something around five minutes per problem might be reasonable.
Do the problems on your sample exam.
Keep an eye on the clock, just like you would at the real exam.
If you run out of time, stop.
Check your answers in the back of the book to grade your exam.
No partial credit!
Enjoy the reward or suffer the punishment, as appropriate.
Repeat if necessary and possible.

The idea is to set up an environment as much like a real exam as you can make it, including time pressure and consequences for both good and bad results.
You should do better if you prepare in the situation where you'll have to perform.
By the way, you can also prepare for quizzes using this technique, although probably on a smaller scale.

Final Remarks

Don't get behind.
In math, new ideas almost always build on earlier ones, so it's very difficult to catch up.
You need to understand, not memorize, so cramming simply doesn't work.
Do the work every day and it's much easier.

Put another way: Math is like a box of chocolates. If you try to eat the whole thing at once you'll make yourself sick, but a bit at a time is great.