Ah, heck. It's not that hard. Get you a couple supports for the arrow shaft and be sure they're set up so you can work on the extreme end of the arrow without a support getting in the way. Also be sure the supports won't mar the shaft in any way.
Get a carriage of some kind to hold the thread and give it tension, reliable tension. Too much tension and you'll break the thread, too little and the thread gets all wonky.
Be sure to measure where you want the thread to start and stop. If you do different lengths on each arrow it won't look very good.
Learn how to start and end the thread wrap. When pulling the thread back under itself at the end use a strong enough pull material that it won't break in mid-pull, otherwise the dog will learn some new words. This also relates to not wrapping so tightly that you can't pull the thread under.
Learn about burnishing the thread, it'll make a world of difference in the final look. Burnishing can take it from "okay" to "holy crap, that's incredible!" Always be sure to lay the thread properly as you wrap. It's pretty difficult to go back and fix something you did an inch ago.
You may want to use color preserver, depending upon the thread you're using and the appearance you want. Oh, yeah... thread. Lots of different kinds and sizes out there, some easier to work with than others. Be sure to order enough, it's pretty frustrating to run out in the middle of the project.
Don't put the final finish on so thick that it drips, unless you have something to rotate the arrow like it's on a bbq spit as the finish dries.
Heck, you're gonna have lots of fun!
Guy