Well, the first step is to get a Manual. Don't bother with E-bay since most there are used and out of date. Helm Inc.
sells manuals but I don't know if theTRX90 is there.
Since I can't find my manual, and I'm rushing to get loaded and go to riding at Durhamtown (12/3/04), I'll try to help from memory. The chain tensioner is a spring loaded plastic shoe that presses against the chain. There is a service limit on the spring and if it becomes too short, you need to replace it. It's also possible that oil pressure is used to tension the chain in addition to the spring. To removed the spring, remove the tensioner bolt that is on the bottom of the engine just inside of the gear shifter. It's a 14mm bolt and it sits at an angle. The oil drain plug is near it but it's a 17mm bolt and it points straight down. Be careful when removing the tensioner bolt because it's spring loaded and i think there is a part on the end that could fall off and get lost. If that part is missing, you'll get lots of noise until the chain jumps timing and then it's a much bigger problem. If that part is missing, you've solved it! You could call a local dealer and ask them for the service limit on the spring and (hopefully) they will tell you. If the spring is too short, replace it.
The other thing to do is to check the cam sprocket at the top of the motor. It's behind the big round cover on the left hand side of the head. It's held on by a long 10mm bolt from the other (right) side of the motor. The bolt is right next to the spark plug boot and is the only one you need to take out to remove the cam-chain cover. A visual inspection will tell if anything is wrong there.
On the other end of the cam is the auto compression release mechanism that makes the 90 easier to start. It's possible that is is broken and making noise. Otherwise, I'd make sure the oil is fresh and full and oil filter mechanism is clean. You'll need a manual to do this too. If you go to a Honda dealer, they migh sell you their used manual. It won't hurt to ask. They might even have a 3rd party manual for sale on the shelf. I've even seen ATV manuals at a big chain auto parts store (Pep-Boys, Auto Zone etc..). Give them a try too!
Hope this helps!