What cable do I need to run from my main breaker in the house underground in schedule 40 conduit to my garage?
Have you tried searching the site? The panel feeder size question has been answered many times. Here's one such example.

Is you're planning to pull a cable, you'll use 3-3-3-5 USE cable with copper conductors (1-1-1-3 for aluminum). If you're pulling individual wires, you'll want four 3 AWG THWN wires (hot, hot, neutral, ground)(black, red, white, green) (1 AWG for aluminum).  If the run is going to be really long, you'll want to calculate the voltage drop and adjust the conductor size accordingly.

If you use the 3-3-3-5 USE cable, you don't need conduit. If you want to install it in conduit, you'll need 1 1/4" schedule 40 PVC. If you use individual THWN wires, you'll also use 1 1/4" schedule 40 PVC.

You'll have to keep the grounded (neutral), and grounding bars separate in the secondary panel.

You'll have to install a grounding electrode system at the garage, and bond the equipment and grounding conductor to it.

NOTES: This is a very broad, and generalized overview, which lacks specific details for your particular situation. You may need the advice of a licensed Electrician, to provide a more detailed plan based on the actual job site.