Take the required live load per SF plus the dead load per SF and add them together.
Determine the contributing area, which is half the span from the header to the back wall.
Multiply by the total load per SF.
You low have the total load per lineal foot on the header beam.
Find a chart or table, for the strength of beam you are going to use, and based on the span and load, determine the beam you want to use. You will have to choose a deflection limit for the live and total loads.
Typically you will use a double LVL beam, fastened together as specified, so look for beam sizes that will support loads that are half the required ones.
Here's a chart I use:
http://parr.com/PDFs/LP%20LVL%201.9E.pdf
Any other method is a wild-assed guess, and just plain dumb.
Note that this is if the roof framing bears on the header. Otherwise the post above this is correct. In that case, the loads are substantially lower and dimentional lumber could likely be used.
Bill