The answer is “not much!” There is very little maintenance required on a well designed solar electric battery charging system. Solar panels have no moving parts to wear out, no fuel to consume and no filters to replace. All you have to do is clean them occasionally with a non-abrasive cleaner and check the mounts and fasteners to make sure they are tight. Vibration, expansion and contraction from temperature changes have a way of loosening up hardware.
Modern charge controllers also have no moving parts to wear out since most are solid state electronics. However, you might want to check the wire connections once a year to make sure they are clean and secure. A loose connection causes resistance and heat, both of which are detrimental to performance.
You should check the battery water level at least quarterly (preferably monthly) and add only pure, distilled water when necessary. The batteries and the wire connections made on or near them are where most of the maintenance is needed. This is because when batteries gas some of the sulfuric acid in the electrolyte might escape as an acid mist and land on the terminals and cause some corrosion. Inspect the wire connections and clean away any corrosion you find. Clean the terminals and make sure all connections at the battery are snug. This unpleasant task is unnecessary if you are using maintenance free Lifeline AGM batteries.