There are definitely different level of sponsorships. The elite players get free products and monetary incentives too. Other levels might just get free products and some will get products at a greatly discounted price. Some sponsorships could include paying for tournament fees, etc. It all boils down to your level of play (& potential) plus your level of involvement in the sports.
talk to your coach, he should know some company representatives from their career to hook u up with something.
Take a look at this site http://www.sponsorship-advice.org/home.asp It doesn't tell you how to get in touch with sponsors but you should be able to make a list which should include Manufacturers & Retailers. For example, I know that Central Sports offers sponsorships (goods at discounted prices). I believe that Matt Ross is also sponsored in the same way by Karakal.
There's a distintion between the terms "sponsored" and "terms". Sponsored = contract, company pays person xxx money to use equipment. You have to be really good in badminton to get it and you must use their equipment according to the contract. Terms = company agrees to let you buy equipment off them for cheap - maybe 4 racquets a year. I think no strict obligations on the usage. Much more common. Ask county players in England about it; most should have terms if top county level. Looking at National level standard to get sponsorship.
You should be good enough, that is if being ranked 8th is 8th for "open" play. However if it were in an age category (juniors), it might be a different story. I wouldn't say I'm good because I'm ranked 17th in under 19
As Cheung pointed out earlier, there are terms and sponsorship. Companies like Yonex will take all the first seeds in an age band and sponsor them ie. they will get some rackets, t-shirts and accessories for free as long as the results come in. The remainder ie. the next three or so in the age band get sponsored by smaller companies trying to get market share and their names noticed. Terms are the more common ways in which players and coaches are linked with companies. The player/coach gets cheap gear at a large discount (probably about cost price of the item or slightly cheaper) and the company still covers the cost of the pieces that are in the terms agreement up to a certain level of pieces per season/year. Again it is probably best to check with Matt as he gets some terms from suppliers.
just play in major turnaments and usually there are reps from the companies there, if they like how you play then somethines they will offer you a sponsorship