If your toilet clogs, you can usually use a plunger to push the blockage through the system. Avoid flushing the toilet when clogged, as this could cause the toilet to overflow.
If other drains in your rental are clogged or draining slowly, you can use a drain cleaning tool to attempt to clear debris from the pipe. These are available in most hardware stores. Be careful when using cleaning products, as some corrosive products could cause damage to the plumbing system.