Care for a garden tiller is about the same as for a gasoline operated lawn mower.
Your manual should provide you specific instructions for maintenance but the following should apply.
Clean the mud off your tiller after every use.
Always inspect the tiller tines before you operate the tiller for looseness or damage.
If you strike a rock or object with your tiller you should inspect the tines for damage.
Store the tiller in a dry warm place like your garage.
If you store your tiller in a shed over the winter you should winterize your tiller by removing all of its gasoline and changing its oil every season will be mandatory.
At the end of the season a light coating of spray paint will protect the tiller blades from rust.
Change your spark plug at suggested hours of use. It is not normally necessary to change your plug every year if you only use your tiller a few hours per year.
Change or clean your air filter on a regular basis. Some air filters are a foam material that can be reused after cleaning however this foam will break down over the years and require replacing. Figure on 5 years maximum for a foam filter.
Always check the pressure in your tires before you start the season. Tires can look well inflated but be down in pressure more then 25%. Although they may feel pumped up you may find yourself with a flat tire if you try to operate the tiller and the rubber tire slips off of the wheel hub. This will not be a fun experience so put a gauge on it before you get to work.