There is no way you can train in Muay Thai on your own unless you have all the right supplies. Sure, you will not have much of an issue if you are taking a dedicated class, because they will have the supplies ready for you to use. At most you may need to get a pair of gloves for yourself instead of always borrowing the old ones they have on site. But if you want to really get better at Muay Thai, you may want to train independently and away from those classes as well. And here is the time when you need to get certain supplies.
One of the things you will absolutely need to get if you want to train outside of class is the Muay Thai pads. These are really wonderful and proper pads that you can use if you are going to train with another person. You can either have a friend or family member help you out as you are doing your own training, or you can pair up with someone else you may have met in class and you can both train together. In either case, we feel as though you can really help each other out in a big way, or you can have someone who is solely helping you as you look to become better at the sport.
So what does the pad do and why do you need it? The reason for the pad is because you need a surface that the person who is training can punch and kick. After all, you do not want to really hurt each other when you are practicing together, and you most definitely cannot be punching and kicking someone who is merely helping you train! So the pad is almost like a moving punching bag that the other person has a firm grip on.