First the terminology…
You’re asking about the “coils”; the ‘compressor’ is essentially the ‘engine’ (more accurately, a vapor pump) that pumps the refrigerant through the system. You need not concern yourself with the compressor–that’s the job of a service technician.
As to those coils…
Outside, likely in the backyard, is the condensing coil. (the whole unit, which includes the condensing coil, fan, compressor and electrical stuff is called the condensor) As to maintenence you can do, simply hose it off periodically with a garden hose. If you keep the outside coil clean it will operate at peak efficiency and extend it’s life. You can spray right into the coil—even when it’s running. (It runs in the rain, right?) Just be careful not to spray into the electrical motor, or into the cabinet door. Spray right into the coil. One caution: high velocity hoses/sprayers may bend over the “fins” on the coil. Be patient and don’t go mongo with super high velocity. Spray it off when it’s dirty with grass, cottonwood etc and you’ll be cool.
Inside, is the evaporator coil. (simply called the evaporator) You’re right, you can’t (easliy anyway) get to it to clean it. It may be in the duct, in which case it will be right on top, or right below the furnace. It’s easy to identify: 2 copper lines run to it; called the lineset. That’s an uncased coil. If those copper lines run into a painted cabinet that looks like it matches the furnace, that a cased coil. If you have a cased coil, you may be able to remove some screws from the front, remove the cover and 'slide" the coil out. That’s not always easy—remember those 2 copper lines are still welded to the coil. In some homes however, the access is easy enough that the homeowner can do it. Most of the times however, it’s best left to a service technician.
It may not need to be cleaned however. A skilled service technician will be able to tell—in either heating or cooling mode—whether there is reduced airflow; a sure sign of a dirty evaporator. (assuming the filters are clean and too many registers aren’t closed) IMO, it’s best checked in the cooling mode. If you have concerns, have a service technician go over your system early this summer when the temperature is 80ish or higher. (if the weather is cooler, reschedule. it really is best when the temp outside is at that point or higher)
Ask the service to check to see if he has any concerns about airflow—he’ll be able to diagnose this from looking at system pressures, etc.
If you’re concerned, and just want some peace of mind, it should take a service tech around 2 hours to uninstall, clean and reinstall. At $75/hr plus travel, and some nominal material costs we would charge around $200-$250, and may be higher if access is difficult. (prices vary wildly by region, contractor,etc, YMMV)
If you haven’t had your system looked at recently, it’s worth the investment to have it checked early this summer. We are in the midwest (SW Ohio) and most of our competitors charge between $75-$89 for a ‘tune up.’ (we charge $89) YMMV.
Hope that helps. Let me know if other questions.