Search for local barns that would be willing to have a deal where you work and they let you ride. If you do a great job then they might recommend you to take care of horses at another barn while the owners away or something like that. Good luck!
You work hard. Start of in small riding schools, then livery yards and then competition yards. Ride whatever you can, whenever you can (within your experience level). Don't say no to the nags, every horse teaches you something different. Get educated where you can. And remember, someone who is used to working for what they have and can ride a variety of horses is going to be much better off in the long run than someone who is handed everything and is comfortable riding only one horse.
Try to see if their are any shares/ part loans near you. You may have to make a slight financial contribution but it shouldn’t be too much and you may have to muck out. You can set a certain amount of days a week and you can go up to the horse and ride. (I did this for about a year and it really helped my riding)
It's hard, but try to find an owner who has not enough time and will let you ride his, or a club that has some good horses and will let you show them