In a bigger Poway home with several bathrooms, a toilet in a guest bath can run for weeks before anyone notices. The signs are the same everywhere. A tank that refills on its own means a worn flapper. A toilet that won't stop running after a flush means the fill valve. A bowl that rocks means loose bolts or a wax seal that's starting to fail, and water around the base means the seal has already failed or the supply line has a leak.
Nearly all of that is repair work. Flappers, fill valves, handles and seals are replaced individually, and a sound toilet can stay in service for years with new parts. A new toilet makes sense for cracked porcelain, a toilet that keeps needing repairs, or an upgrade to a newer, lower flow model, with a bidet seat added if you want one. You'll hear which one fits before anything is done.
If a toilet keeps backing up, that's usually a drain line problem rather than the toilet, and it's taken care of as drain cleaning. For everything on the toilet itself, a licensed contractor does the work, with the options laid out in plain English and the decision left to you.