How to remove SD card safely
The physical construction of the card and socket are designed such that power to the card is cycled properly when the card is inserted and removed. The only thing the firmware has to do is to stop writing to the card before it is removed.

Unexpected removal can cause a problem in "larger" systems (e.g. cellphones or PCs) because they may have structures open on the card that are not yet complete, but small embedded systems typically do not have the capability to do so and so once all writes are completed the card can be removed.

Detection of non-presence of a card is another issue though, and the firmware will have to be designed to not fail in such a situation.