What kind of wire do i need to run to a shed?

I am planning on adding electricity in a car port 125 from the breaker box. I want to use lights and a circular saw. What size/amps of wire do i need to run?

For that distance I would use a 20 amp circuit breaker and 12 gauge wire.

Do yourself and any future homeowner a favor and run a 3/4" pvc pipe out to the carport. Someday it'll become a garage, and more power will be wanted. (If it were me, I'd put in 1")

You need to use pvc to "run" the (direct-burial) wire down to the ground from where it exits the house anyway,- just take it the rest of the way to a plastic, or "bell" box.

Should your wire get damaged, you'll have to replace it.
If the pvc got damaged, you could fix it much easier.

If an underground circuit is limited to 120 volts, and is GFCI protected, the pipe only needs to be buried 6".

You should be fine with 14 ga, but 12 ga. will allow more application flexibility in the future.

14 ga. handles 15 amps,
12 ga. handles 20 amps.

Note: Some electrical jurisdictions require a minimum wire size of #12 A.W.G. and do not allow the use of #14. Check with your local electrical authority to determine if this applies to your area.

If you are burying the cable, check the following resource:
http://www.dulley.com/diy/dw107.htm