Really easy cheat sheet --

Stay on the middle ring (where the pedals turn) most of the time. You can shift through all 9 cogs at the back.

If you are going uphill: drop down to the smallest ring. Use the largest 3-4 cogs.

If you are going downhill, or really fast: go up to the biggest chain ring. Use the smallest 3-4 cogs.

You don't really get 27 unique speeds: there is a large overlap in gears between the different chainring / cog combinations. You only get the unique gears at the "fast" end (large chainring, smallest few cogs) and the "slow" end (small chainring, largest few cogs). There is no reason to cross-chain, because you have those gears on your middle chainring, and should not be shifting all the way through the large or small chainring.