कोशी का प्रवेश द्वार — मानसी जं० - Prabhat Sharan

The other answers already cover most of the ways the railways move their locos to the shed for maintenance.

One more way this is done is by having some trains have loco changes at the stations close to the sheds. In these cases, normally a loco change is not needed at those stations.

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popular examples for this, back in the day were -
KK express - When KK was running with GTL twins, the Bangalore-bound KK used to change to a new set of GTL twin ALCOs at Guntakal (D-loco to D-loco change). These locos would continue with the train to Bangalore, then start with it in the return journey and run till MMR. From there, they would be attached to Ajanta express, go to SC and participate in many other LSAs, before finally returning to GTL with KK.

MLDT - Quite a few NFR trains used to switch from D-lcoo to D-loco at Malda Town. These trains were used for moving the MLDT diesels to their home-
shed.

Kerala express - Kerala express famously had a loco change at Erode. It used to switch from an ED WAP4 to a freshly maintained WAP4 at Erode for its roundtrip to Delhi. Within Kerala, some passengers like the ERS-SRR passenger were used for moving locomotives.

The SBC-AJJ passenger was also used for moving locos to AJJ shed.