As others have said, the best thing is a comprehensive First Aid course. Knowledge is very lightweight.

As far as a kit goes, the most common and most likely "injuries" will be minor cuts, scrapes, blisters etc. I carry a few different sizes of Band-Aids, antiseptic wipes, antibiotic ointment, blister pads, a couple gauze pads and tape, and some OTC meds such as Advil, Immodium etc.