Taking care of your tankless water heater is very simple. Because of the lack of space they take up and how much smaller they are then a regular water heater not only is cleaning and servicing going to be less often, but it is also going to be much faster. Parts are smaller, making it easier to fix and also install when it's time for a new unit (if ever need be).
Depending on how hard your water is in your specific area will depend ultimately how often your tankless water heater will need to be serviced. Hard water causes calcium buildup and the harder the water is the more buildup will accumulate. Normally, to keep your water heater running smoothly, a servicing should be scheduled once a year.
Also, depending on the type of water heater you have the screen filter should be checked periodically for debris. Again, amount of time between the checks of this filter will depend on your water quality.
You may also want to flush the unit periodically. This can help keep your unit free of scale and lime. Always refer to your owners manual for tips and care about your tankless water heater.
Of course, over time you may want to consider not just servicing, but replacing your water heater. Because a tankless water heater is energy efficient it will last longer, but not forever. Contact either a plumber or the original installer for service needs. Many different brands offer 24/7 support and/or online trouble shooting if anything should go wrong with the unit.
Having continuous hot water is something many prefer so taking care of your tankless water heater is important. Schedule a servicing at least once a year. The rest of the maintenance (if any) will need to be done depending on your water. Soft water, less often. Hard water, more often.