Compressed text on the SNES always needs to be decompressed and stored somewhere. Since you can't write to ROM, it's stored in RAM.
That's where you can start to find it. In the very least, the game will have the current string decompressed in RAM. If you're lucky, you may find the entire text block.
Anyway, you'll need to find the address in RAM that the text is decompressed to. Then you can use that when looking in trace files or using a debugger to look at the code and see how it got there. Ultimately, you'll find text is read from the ROM at some location and run through a routine and then stored in that location at RAM before it's printed to the screen.
SOMETIMES you can crack the compression simply by examining the compressed data in the ROM, but more often then not, especially since you're new, you'll probably need to look a trace file of the decompression routine and try and figure out what it's doing.
Also, you don't necessarily need to know how the compression works sometimes. You can hack the routine to read uncompressed text from the ROM. However, depending on your game, this may or may no be easily feasible.
All of this is secondary. The first thing you need to do is find either the location in RAM the uncompressed text is or the place in the ROM where the compressed text is, whichever you can locate first. You need to start somewhere.
Relative searching can sometimes find a portion of compressed text in the ROM right off the bat. To have any luck with that, you'd want to look up the first word in the first string of the game. It has a high chance of not being compressed since compression works by eliminating redundancy. However, there is no redundancy yet at the very start of the data stream(Unless the game uses dictionary on top of the main compression routine and the first word happens to be a dictionary entry).