A large part of my refactoring is composing methods to package code properly. Almost all the time the problems come from methods that are too long. Long methods are troublesome because they often contain lots of information, which gets buried by the complex logic that usually gets dragged in. The key refactoring is Extract Method, which takes a clump of code and turns it into its own method. Inline Method is essentially the opposite. You take a method call and replace it with the body of the code. I need Inline Method when I've done multiple extractions and realize some of the resulting methods are no longer pulling their weight or if I need to reorganize the way I've broken down methods.
The biggest problem with Extract Method is dealing with local variables, and temps are one of the main sources of this issue. When I'm working on a method, I like Replace Temp with Query to get rid of any temporary variables that I can remove. If the temp is used for many things, I use Split Temporary Variable first to make the temp easier to replace.
Sometimes, however, the temporary variables are just too tangled to replace. I need Replace Method with Method Object. This allows me to break up even the most tangled method, at the cost of introducing a new class for the job.
Parameters are less of a problem than temps, provided you don't assign to them. If you do, you need Remove Assignments to Parameters.
Once the method is broken down, I can understand how it works much better. I may also find that the algorithm can be improved to make it clearer. I then use Substitute Algorithm to introduce the clearer algorithm.