I want to run a 30 amp breaker to a sub panel in my shed. That will run a couple of outlets shop light and a 20amp exhaust fan. The run is 150ft. Will that work?

NOPE. Consider a 40 amp circuit to the sub panel. You will need 4 wires, 3 #6 and 1 #8 for the ground. You will also need a grounding rod. Have you done this type of work before?

A 30A feeder is the minimum size you can run, so #10 is OK if the bare minimum is OK for you. Thing is, 10/2 is NOT OK. You would need 10/3 to have a 120/240v sub-panel.
A 120v only panel is technically code legal but makes absolutely no sense to install.

Like Missouri said, a grounding electrode (ground rod) is required in any detached building with a sub-panel.

I have done some but not to a sub panel so you are saying I need #6 wire and #8? Why so big because of the run? Thanks For the last answer

Correct, the #10 will result in too high a voltage drop for a 150 foot run.