Just going to cite my references here, Med Student and my sister is a paramedic.
Clean the wound thoroughly, give it a quick clean with an antiseptic wash, but you don't need to leave this on for more than 2mins. The idea is to create a sterile environment, but antiseptics attack cells fairly indiscriminately so they can slow healing times if applied consistently. After that, we generally recommend wet wound healing, Solosite is amazing stuff, it's essentially just water in gel form. Slap that on the wound, cover it with a decent non stick dressing, if it's on a nice flat area like forearms, or shins, waterproof it and don't think about it for days on end.
The moisture is a better environment for the new skin to grow back in, as long as you sterilised correctly, it won't infect. Obviously keep an eye out for any burning or inflamation on the wound, the solosite can look a little yellow/white as the skin grows back, but this is to be expected. A lot of people can mistake this for pus, but it generally isn't. If you want to go all out, use solosite in conjunction with a....forget what they're called, but it's like a silicone net that you throw over the wound that helps keep the moisture more localised. Expensive, can potentially re-use them if you steralise and store them in water afterwards, but you'll got from raw wound to new skin in a week on a treatment plan like that.
