Proper testing requires a multi-tiered approach. Your testing process should take these tiers into consideration.
There are at least a couple of ways to look at this. One is called the testing triangle, and describes a structure where numerous unit tests are at the bottom, and a few manual tests are at the peak. Between those two extremes are integration tests and acceptance tests.
Another approach to looking at how to focus your testing efforts is through the agile testing quadrant. This approach has you organizing your test by what they test -- whether they are business facing or technology facing (Y axis), and whether they serve to critique the product or support the programming team (x axis).
(Note: these two ways of looking at testing aren't mutually exclusive -- they are just two ways to look at the problem)
So, your first step should be to decide how you are going to test. Are you going to focus on manual testing? Unit testing? Can you automated your user acceptance tests? If you are like most programming teams, you have limited resources so you will need to decide how much effort to put into each type of test.
Each of those types of tests will then require their own plan, though you don't necessarily need a formal, written plan. For example, the plan for unit testing would be simply that developers should write unit tests for any code they write, and they should be run after every build.