What's the best way for me to clean a cut?

Depends: How did you get the cut? Is it an animal bite, a clean knife, some sharp object you bumped against, etc? This will dictate what cleaning is necessary. A cut that bled a lot is somewhat self cleaning and then you can flush it out with fresh water. If the cut is too big, you might need to hold the edges together with tape or seek help to have it sewn together.