Getting into the Groove

The common version of this expression is "get into a groove," which means to get used to a routine, to get settled into a comfortable pace doing something, to hit one's stride.

It would normally have a positive connotation in American English ("I got into a groove about the middle of the race"), but you could use it to imply that you are unable to get out of the routine, and in British English to "be in a groove" may more often relate to boredom.

See these definitions:

groove, 3:

a fixed routine: to get into a groove.

groove, 3:

A settled routine: got into the groove of a nine-to-five job.
in the groove: Slang - Performing exceptionally well.

The expression "get into the groove", on the other hand, can mean to have fun or to get with the times, usually in a positive way. This phrase is probably a bit dated (1985 Madonna, anyone?). "The groove" is a reference to musical rhythm, probably from the physical groove in a record. This discussion sums it up pretty well:

To "get in the groove " means to enter into the spirit of the situation or circumstance of the moment. The groove is really the track on an old record in which the needle of the record player had to ride in order to reproduce the music--so the meaning is figurative.

To "get into the groove" is generally a positive thing; its etymology comes from dance and live music, and it implies finding the beat and rhythm of music being played and moving to it. That usage in turn most likely stemmed from the use of vinyl records up until the mid 1990s; vinyl EPs/LPs have a literal "groove" with the analog sound wave pattern moulded into it and picked up by a needle; "get into the groove" may thus have been used literally to mean "put the record on the player and drop the needle in the groove".

It is now used figuratively to refer to finding and following any sort of rhythm, or finding one's place in a group. It is roughly synonymous with "go with the flow" or "find your rhythm".