First thing drain your carburetors you could have water from condensation that has accumulated in the fuel tank. There will be a drain screw directly on the bottom of the carburetors. It is almost guaranteed to be a Phillips or hex screw.
Second thing go ahead get a new fuel filter won't solve your problem but could cut off confounding factors. If your bike doesn't have one get an inline fuel filter add one (Prob less than $3). Drain the fuel tank completely at this time.
Past here it might save you money in the long run to simply get a repair manual. The Clymer one will probably be fine on a bike this old, you could price an OEM manual too though, if similar in price maybe get the OEM.
Now you likely need to clean out the carburetors and possibly replace floats/ float valve (could be what is causing the sporadic rpm bouncing). See if a carburetor kit is available for the bike at your local dealer. If so, ordering it will save you a good deal of hassle. If its not you will have replace any parts individually. You can go ahead and assume you might need a new float bowl o-ring/gasket as they aren't always good to go back on after you take them off.