You then conclude that if the assumption is true, then the other proposition is true. Then you manage to derive q, using the assumption. You would then go on to try to derive a contradiction. And therefore, you conclude that p must be true. The general principle is that any assumption that leads you to a contradiction must be false.
Indirect proof is an extremely useful method, both in logic and in the real world.
Example of an indirect proof The book has an example on p105. Here is another example. It is not among the 7 rules I listed above, however. Usually, the assumption will just be the negation of the conclusion you're trying to get to. Notice that step 8 is of that form.