What's the best way to treat a bad cut on my finger tip?should i also let it air out once in a while?

Cut on finger: Make sure your tetanus immunization is within 5 years if a dirty wound, otherwise 10 years of receiving it first. Most important is to stop bleeding and keep it clean from dirt or other contaminants. Use a sterile bandage with antibiotic ointment to help it heal. Air exposure is fine, just not contact with contaminated surfaces, dirt, or other toxic substances. Air, water, sterile band aids only.

Cut: When was your tetanus shot? You may need a booster if more than 5 yrs. injury to the finger should be examined since there can tendon damage if the injury was with a sharp edge and deep. If the injury was from a contaminated device you may need abx. Best to see a doc. Till then keep it clean and dry. Avoid pulling skin impairs healing.