How to treat a wound?

That is a: rather broad question and begs many answers depending on specifics. Generally, one treats a wound to maximize the individual's inherent healing rates while minimizing re-injury or ongoing injury. More specifics in the question will get more specific answers.

Wound Care: Stop bleeding by applying pressure. Rinse wound w clean water. Clean surrounding skin w soap & water on wash cloth. Remove debris w tweezers. If material remains in wound – seek medical care. Apply antibiotic ointment. Initially cover w bandage until some healing has occurred. Change bandage when soiled/ wet or at least daily. Need tetanus shot if you haven't had one in last 10 years, don't know

Multifactorial: Stop the bleeding. wash with soap and water. apply antibiotic ointment. cover with a dry dressing. change daily. check your tetanus status. see a doctor if things worsen. sounds like it may have needed sutures from the start.