Hi I have a 1978 Suzuki GS 550 how do I check the charging system?

Check/test the ignition pickup coil on the end of the crankshaft under the small cover.

I have always used 25 thou or 0.6mm gap on these bikes and had no problems even when racing.

Start by checking the stater output from there the voltage regulator output.
stater voltage is ac. and should be 3 yellow wires going to the voltage regulator.
This voltage will hurt you!
It is a good start

if it takes a charge off the bike on the bench, (if not replace it) check your fuses.If you still cant run it, the volt regulator (rectifier) may be bad.

There are points on it if it is the one I am thinking it is by the picture. 1978-1982 ish? They should be located under a five inch or so round cover on the right side of the engine, just infront of the rear brake pedal. Be carefull removing them, there is a special tool to remove the plate the is in the back of them. Just make sure they are not rusted and check the gap on them ( I would tell you what the gap is supposed to be, but I don't know).

yep