1. When I turned 15, I got a job. I did anything I could to get a job. When you're 15, it's not difficult. Fast food restaurants are ALWAYS hiring, and I don't know about where you live, but around here, if you drive down the road and stop at farms, a lot of them will hire you on the spot.
2. This summer I started looking at horses. I started with Craigslist. There are suprisingly good quality beginner horses on there for stunningly low prices. Then one day, I fell in love with a beautiful black Morgan gelding. Fast forward a month or so, and he was mine. A lot of owners who are committed to selling their horse will let you make a deposit. I did. I payed half his price + the trailoring fee to bring him down. That was $350, which is about a month of pay at minimum wage.
3. After I found one I liked, I started saving. Almost all of my money went into the bank. Most of this I planned to use for vet bills. I bought used tack. Used tack is your friend! I bought my saddles for $100 and $120. Both came with headstalls, etc.
4. So now I merely needed somewhere to keep him. If you have friends with horses, talk to them first before looking at boarding stables. They may be your cheaper option. I currently board my boy at my boyfriend's house with his sister's mare. I pay only the cost of hay per month, about $75, but I also have to feed once a day, water horses twice a week, break ice, etc. etc.
5. The hard part is going to be when you think about vet costs. An emergency could happen and the bill could end up being $3000 or more. You have to KNOW how you're going to pay those bills. Are you prepared to sell your horse if you have no other way out?
Just like you are doing, I gave up everything to get my horse. It gets alot easier once the costs of the horse and tack are out of the way. Then you just have little things like board, trimming, and worming to worry about. Also, regular checkups and teeth floating every now and again. The advice I have for you is this: There is always a way if you are willing to go the distance.