Welcome to the forum!!
Although the degree of collection called for varies from discipline to discipline, the basic idea stays the same. Collection is the end result of all-around good riding and muscle building. Take a look at the Dressage board as well - even though it is more dressage-oriented, the basic concepts are the same whether you want to ride dressage, WP, jump, or run barrels.
Although this is a huge topic, I'll first direct you towards the Training Scale. Leaving aside the detailed differences between French and German schools and whatnot, the Training Scale basically runs like this:
Collection is the "capstone" of the training scale, and is only possible if the horse is forward (more than just Energizer-Bunny speedy), relaxed and in rhythm, supple, accepting of contact (more than just hands), moving with impulsion, and straight. The tough part of the training-scale concept is that everything is worked on at once, so to speak. We don't just master suppleness without working on something else. That being said, each step builds on the one before it - if the horse isn't travelling forward with relaxation and rhythm, he's going to have a very hard time suppling and accepting contact.
So, first off, is your mare moving truly forward, relaxed and with steady rhythmic gaits? If not, there's your starting point. You really can't "make" a horse do anything, much less collect in any true and proper sense of the word.
Here are a few links to sites and books that might be helpful to you:
Http://www.amazon.com/Dressage-Exercises-Horse-Rider-ebook/dp/B003WOL56Y/ref=sr_1_1?s=books&ie=UTF8&qid=1318180012&sr=1-1 The Art of Classical Riding--Dressage Training for Horse and Rider ::: Sustainable Dressage - - Welcome to my Site about Sustainable Dressage! :::
Apologies for all the dressage-centric resources... honestly, the point is the same. A Paint responds the same way as a TB or a Warmblood - the only difference is in the degree of true collection that constitutes a "collected horse" in a specific discipline. Small-d dressage is good for every sound horse, and can be done in any kind of saddle.
Good luck, and happy riding!!