Often times the biggest hurdle to getting riding lessons is the cost. Horseback riding lessons often cost $50-$150 for a private one hour lesson which is difficult for many to afford. Luckily, there are many ways to get cheaper even free riding lessons. None of the advice I am giving is for those needing equine therapy as that is different from riding lessons.
You will first want to look for equine rescues and barns providing equine therapy. You might be wondering why I am telling you to look for horse rescues and equine therapy but there is actually a really good reason for this. Many equine rescues need volunteers to help care for their horses and are willing to let you ride the horses that can be ridden for free in exchange for helping out. Now not every equine rescue is going to have this as an option and you don't want to just ask them if you can ride their horses. Rather send a polite email (with parent permission) and express an interest in volunteering. If they agree to you volunteering you can either ask about riding opportunities when you go out to meet everyone or you can volunteer a few times and then ask about riding.
Similar to horse rescues many barns that offer equine therapy need volunteers to help take care of horses and to help disabled riders. Many of these equine therapy barns just have riders walk on the horses so they will have volunteers ride the horses to keep muscle on them or just as a thank you to the horse loving volunteers. Just like with the horse rescue don't say you want riding lessons in that initial email but rather ask them in person at the end of your tour or after volunteering for a few days if there are riding opportunities for volunteers.
If you have contacted equine rescues and equine therapy barns but haven't had success, or don't have any near you, or just want to ride at a barn instead of volunteering then you will want to next look to barns in your area. When looking at barns in your area I recommend looking at as many options as possible and also looking at different disciplines, especially if you are a beginner rider and just need to learn the basics for a while. When looking for barns in your area search for western riding lessons, english riding lessons, saddleseat riding lessons, even gaited horses riding lessons, etc. You are going to want to search every riding lesson option available and then fill in the worksheet portion that includes writing down the barn name, the cost of their riding lessons, if they have a working student program, and much more. Some barns are going to be much more affordable than others.
Just because a barn doesn't have a working student position on their website doesn't mean they don't have a working student position. The best thing you can do is reach out to a barn (with parent permission) and ask them if they offer a working student position. A working student position is one where you help out at the barn doing things like feeding horses, grooming, tacking up, untacking, bathing horses, cleaning tack, cleaning stalls, sweeping the barn, turning horses out, and really anything else that needs to be done around the barn in exchange for riding horses for free or for a reduced lesson fee.
There is also the cost for equipment and gear, which can get quite expensive. Luckily there are many ways for you to get cheaper/free gear, which you can read about on the horse gifts page under the discount and used horse tack, equestrian apparel, and barn items section. Make sure you fill in the section on the worksheet that talks about riding equipment with what you have found and the price. Another great way to find inexpensive items is to call local tack stores and ask them if they have a consignment section or if they have any big annual sales.
Now that you have a list of horse rescues/equine therapy places/barns along with cost of lessons at different barns and an estimate of how much the riding clothes/equipment will cost you will be better prepared to talk to your parents about the cost of horseback riding. But before talking to your parents I recommend filling out the rest of the worksheet.