Firstly you have to have a really good set of results - its no good going cap in hand to people with a few results at local level, you must have lots of top results at cuonty/affiliated shows.
Then, you almost have to approach them with a package, eg, what they get out of sponsoring you, what you are looking for, and what they will get in return. If you want a feed company to supply all your food, and they just get a little sign on your trailer, chances are they will say no. If, however, you can offer them signs on your lorry, logos on jackets, rugs, numnahs etc, things may look up.
It also helps to have some magazine clippings of your achievements - you can add that they will be mentioned if you are interviewed for magazine articles etc.
It is a long and difficult road to sponsorship - I know people who have ridden internationally and cannot get sponsors, and others who hardly compete at all and are tripping over sponsorship offers. A lot has to do with how you sell yourself. If you do get a sponsor, they often like you to be out every weekend, promoting them (as well as yourself) at shows, so you must committ to a busy show schedule.
It helps to know people as well- I got a minor sponsorship deal when a friend started her own company and I got another when our feed man took a liking to me