Lambda the Ultimate

I've been studying the lambda calculus by reading the available texts found doing your basic google search. A question has come up that I have not found a sufficient answer to.

When doing variable substitution in an application ((E1 E2)) it is fairly straight forward if E2 is a variable. When E2 is something more complex, like an abstraction, how do things work with regards to alpha conversion?

Do you first find all the free variables in E2, then rename those that exist free in E1? Or since E2 isn't a variable do not do an alpha conversion stage?

Anyone out there too familiar with lambda calculus, I'd appreciate a little assist.

-Chris