Changi Airport MRT station is accessed directly from Terminal 2, so you're gonna have to go up and take the skytrain from Terminal 1 to get there. Just follow the signs to get there.
The skytrain itself will only take a couple of minutes, and once at Terminal 2, again look for the signs to the MRT/train station.
Changi airport generally has very good signage and information, but if you get lost, just ask any staff you see (English is the common language there).
Once at Changi Airport MRT, take the train west towards the city. (It'll be the green colored East-West line, but this is just FYI, cause Changi is the east most station, so you can't go in the wrong direction or anything.)
Once on the green line, just stop at City Hall or Raffles Place (or whichever part of the city you're heading for, but those are generally the two most common, and interchange with other MRT lines as well).