Unit Step Laplace Transform

Deathfish

Someone give me a crash course on Unit Step Laplace Transform and Inverse Laplace Transform. Need help on the formula:

U(t-a)f(t-a) to (e^-as)F(s)

from what i can deduce, the way to use it is

(Laplace)

- Find a from U(t-a)
- group (t-a) together
- replace (t-a) with ____ (?) What is a suitable symbol?
- work out Laplace
- multiply Laplace with e^-as

(Inverse Laplace)

- Factor out e^-as
- find out what is a from e^-as
- inverse Laplace
- replace t with (t-a)
- multiply with U(t-a)

Just need to know how to use it, not how it works in detail. Tell me if I got it right and any where to improve on. Also need to know a suitable symbol to replace (t-a) as above. Thanks!