Take the battery back out so you can see the belt clearly. Now check on the small idler pulley to make sure the belt is inside of the belt keeper. You may have to loosen the pulley bolt to get the belt inside of the keeper as it is often formed into the arm.
Once you have the belt in the keeper, or if the belt has been in the keeper all along, check to see if the belt is on the top part of the variable pulley. The variable pulley is the one that has the belt from the engine on it too. If you look at the variable pulley you'll see that there is an upper and lower section to it. The part that separates the 2 sections should be able to move up and down easily (when one or both belts are not in place).
If the belt looks good on the variable pulley then check on the transmission pulley (the big one) to make sure the belt is on it all the way around. Often, it is very hard to get the belt onto the transmission pulley on the right side since the pulley is right up close to the frame. In that area, the frame acts as a belt keeper.
If all of that looks good then there is something else going on. I have seen the bearings go out in the variable pulley and cause problems with the belt staying on and/or problems where the speed will not change as it normally does. If you determine that the problem is with the variable pulley, you may want to consider having it repaired by a professional. It can be a bit difficult to get the variable pulley in and out (correctly) and you'll most likely need to raise the back of the tractor (securely) in order to address any problems with the variable pulley.