The fact that it's a Fuji has virtually nothing to do with this.
However, a touring bike from 1984 is very likely to have horizontal rear dropouts (where the rear wheel fits) which makes things much easier to run a singlespeed.
The rear wheel probably takes a freewheel. If so, you can get a singlespeed freewheel and re-space and re-dish the wheel.
Or, you could keep the freewheel currently on the bike and just stick the chain on the gear that you want to use. (This is heavier, but otherwise shouldn't be a problem.)
If you want to simplify things more, you can run a single chainring on your crank.
The main goal with a singlespeed drivetrain is that the sprocket on the rear wheel lines up with the front chainring. That's why I talked about re-spacing the rear wheel if you get a singlespeed freewheel. You may also want to run a single chainring on your crank, and get a new bottom bracket (with shorter spindle) so that the chainring sits closer to the bike's frame.
Sheldon Brown has an excellent and informative page about singlespeed conversions: