What are some tips to keep in mind when solving back of the book exercises?
There are probably lots of similar questions on this site and on mathematics SE. Two suggestions.

Find a friend or group of friends to work on problems with.
Take a look at Polya's How to Solve It for problem solving tips.

I think your goal should be learning from problems, not necessarily solving them faster. Good problems ask for more than  calculating correctly and quickly. If that were all there was to problem solving then computers would be better at it than people.