shower drain is only 1.5"

replacing my shower and new drain has 2" connection.
I know code calls for 2", but this fairly new house apparently got by with a narrow one. It's over the garage, so underneath access isn't too big a deal i guess, but......

what's involved in making it a 2" drain? would i run it over to the toilet drain or tub drain, where it would have a larger diameter pipe?

You need to run it to wherever you need to to make it into a 2" or larger drain pipe. You have to maintain the proper slope and it must be vented before it gets to the next fixture. You might just follow the existing path, since it must eventually get to a larger pipe.

2"

There is absolutely no way we can tell you HOW to increase the pipe to 2", without being at your house or having a very detailed picture.