Once the satellite is nonfunctional how are they removed from orbit?
A "properly" configured satellite is one that was engineered, constructed and launched with sufficient fuel and engines to allow the satellite to be placed into a controlled lower orbit with a known expected point of re-entry.
Once the satellite is low enough to experience increased drag due to atmosphere, it will begin to burn up and/or fall into an ocean.
Not all satellites qualify for the above circumstances. Skylab is one of the more famous examples of "what comes up, must come down" but not necessarily under control.
From the above linked web site:
Even though Skylab was devised for just a nine-year lifespan, NASA failed to build in any control or navigation mechanisms to return the orbiter to terra firma.
@fred_dot_u's answer is only partially true:
It's not reasonably expected for a satellite to be able to deorbit itself since the delta v cost can be very high for GEO orbits (1500m/s).
While LEO satellites are expected to deorbit themselves, generally over the pacific, GEO satellites cannot do this and then are moved into a higher, grave yard orbit.
However, not all satellites are able to do this since failures can (and do) happen before the end of life of the satellite.