The baseboard itself only need cleaning with a vacuum on occasion to get the dust out. Keep the outside clean as you would the rest of the house. Dust, wipe with a damp cloth as needed, keep the air path unobstructed.
The system is set up with an automatic feed and air bleed and an expansion tank of some sort. They require little or no maintenance.
The oil burner should be cleaned and serviced once a year or every 1000 gallon or so. If it has not been done in a while, call a service company or your oil supplier and schedule a cleaning. It will cost about $120 and they will clean the soot, replace the nozzle, change the tank filter, inspect everything. Don't be a pest while he is working, but ask the service guy to show you the main controls, the reset button, etc. Once you know the basics of how it works, you will at least know where to push the reset if the heat goes off in the middle of the night. It may save a service call. It is also best to keep your oil tank at least 1/4 full.
Know where the circulator pump(s) is and that the thermostat turns on the pump to bring hot water to the heaters. When the water circulates cooler water enters the boiler and the internal aquastat tells the burner to start up to make the water hot again while the cycle repeats.
You get extra points knowing you have a boiler and not a furnace. Boilers heat water, furnaces heat air.
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