Dude...first I gotta say I had written a nicely detailed post but my browser crashed before I had a chance to submit it...grrrrr

But here I go again

The best method for applying dye for tie-dyeing is the squeeze bottle. It is not uncommon when you first start out dyeing to over saturate your fabric in an effort to get good saturation and not leave much white. A helpful trick is to get the nozzle into the folds to get color to those inner layers.
Tie-dye is messy(that's part of the fun!) but it is good to have a set-up to help minimize the risk of dye on the table surface getting onto your piece in a place you don't want. I use both a length of wire shelving set on crates and more recently have been placing newspaper on a crate and then putting the piece on that.
Thickening your dye with sodium alginate will also help give you better control over the flow and spread of the dye.
I know I may have told you before but definately check out the
Fiber-Arts Forum. Oh so much info, its kinda crazy!
As far as folds go, it depends on what your are doing and what fabric you use. A good rule of thumb is to keep the height of the folds 1 inch or less and in uniform height. Thicker fabrics and folds that have more layers may require the fold to be a bit larger(higher). Also, keep the layers of fabric together when folding, keeping the fabric damp will help this.
I use 100% cotton twine/yarn. A recent discovery is Lion's Brand cotton yarn. I got a 1 lb cone at Joann's for 10 bucks(if I had remember my coupon it would have been half that!) The thing is huge and will last me forever. Picture a cone of serger thread on steroids

Read as much as you can. This is what I did. It really helped to understand how the dye interacts with the fabric and its environment. I like Ann Johnston's and Elin Noble's books. Buy some and also check out your local library, mine had some good one's that were informative. Fabric-Arts.com also has an awesome DVD
The Art of Tie-Dye and its on sale right now. They also carry another create set of instructional videos by tie-dyers Tom And Martine out of New Mexico. When I first watched the Art of Tie-Dye it was like a light bulb going off in my head, an "AHA" of sorts b/c it was the most helpful to actually see someone designing, folding, and dyeing pieces. Books are great but somehow well detailed diagrams and pictures don't always do the trick.
ANyways...hope this helps and I will cut it short here before my browser crashes again and I lose it all

Kathy