OK. For AQHA, you need her original registration certificate, and you need to check and see who is recorded on it as the most recent current owner. Then you need a transfer form signed by that person as the seller.
If you don't have a transfer form, you can get a transfer form for AQHA here-- http://www.aqha.com/forms/pdf/Transf..._02_01_Web.pdf
Seller needs to sign it, and you need to fill it out with you listed as the buyer.
Then send in the original certificate, the signed transfer, and all fees (transfer fee and membership fee if you are not already an AQHA member) in to AQHA, and AQHA will send back the registration certificate with you listed as the current owner, and you will be listed as the current owner in their records as well.
Make sure the date of sale you list on the transfer of ownership BEFORE the dates you start breeding the mare, so that you are her recorded owner at breeding and foaling time-- that way as the mare owner you can sign the relevant parts of the registration application for your foal.
If you don't have the original certificate, but know the horse's registered name and/or number, you can call AQHA to find out who the current listed owner is, and the current owner would have to sign an affidavit to get a duplicate registration certificate issued, in addition to the signed transfer. http://www.aqha.com/forms/pdf/AffidavitDupCertWEB.pdf