First, the

f x =

part says that f is a function which takes a single parameter, called x.  The other side of the = sign gives the function body: in this case, x + x.  This is exactly the same thing that is expressed by the lambda expression

\x -> x + x

This expression defines a function that takes a single parameter called x, and returns the value of x + x.  The only difference is that with the lambda expression, this function is not given a name.  But you can easily give the function a name (just as you can give any Haskell expression a name) by writing

f = \x -> x + x

In general, writing

g x y z = blah blah

is just a shorthand for

g = \x -> \y -> \z -> blah blah.

That is, it simultaneously creates a function expression, and assigns it a name.

Does that help?
-Brent