I worked in a pharmacy for seven years, and the advice folks have given has been exactly what the pharmacists told our customers.
Clean the wound well with water. Use peroxide if necessary, not alcohol. Use butterfly bandages or wound closures to close it up.
If it is a puncture, soak it in a betadine solution once a night until it heals over. The bottle of betadine will tell you how to mix the solution, it's usually 10%. This seeps in and kills any germs, and a saline solution (tablespoon of salt in a few cups of warm water) will work in a pinch.
If your tetanus shot is out of date, get one. It's cheap insurance for us folks that swing blades around.
The vitamin E oil and rubbing the newly formed scar both work. Rubbing it sends blood to the area and this keeps more tissue from dying or toughening up. Vitamin E softens the skin and keeps it from drying out.
I have a barely noticeable scar on my thigh from when a Benchmade CQC7 tanto bit me (the whole point went in under the skin) and the vitamin E oil took care of it.
Take care and I hope you heal up well!