Buying a used trials motorcycle takes more studying and consideration than buying new, but you can find some great deals if you do your homework. It's important to consider the bike's use and service history, condition and price.
When purchasing a used trials bike, consider whether you want to buy from a dealer or a private seller. There are positives and negatives to both. While you may pay more for the bike through a dealer, the dealership is more likely to offer a warranty and more specialized knowledge about the type of bike you are looking for. They also have a selection of bikes to choose from. Private sellers are typically very knowledgeable of the bike they are selling and may be able to negotiate more on the price, but it's unlikely they offer any kind of warranty on the bike or provide any kind of service after the sale.
No matter where you buy, you want to carefully inspect the bike you are considering and take it for a test drive. Trials bikes are made for obstacle course riding, where the rider's feet can't touch the ground, so they have stiffer suspension and no seats. That means a used trials bike is likely to have more suspension wear than other types of bikes, so you want to examine that carefully when evaluating for possible purchase. Ask for service records so you can see how the bike has been maintained. Also, don't assume that low mileage is a good thing. A bike that sits for long periods with no one riding it can develop mechanical issues from improper storage. Ask to see the title to the bike to make sure that the mileage and title match up.
Don't get too attached to any one bike right away. There are so many dealers and private sellers online and in bricks and mortar that you should keep your options open until you find the one that's just right for you.