Hi,
Buy a multimeter, cheap one <£10 'll do.
Borrow book on bike electrics(library).
Clean all connections.
Charge battery, fit to bike, leave one terminal disconnected.
Measure voltage before connecting other terminal - should read 13.2v DC if batt in good order + fully charged. Connect other terminal, measure again with ignition off(no load), should show same voltage. Less means drain somewhere, possibly through rectifier or zener diode, so disconnect each in turn to isolate faulty part.
Turn ignition on, measure again. There should be small drop in voltage compared to previous measurement(1/2v to 1v). Even with faulty or discharged batt, when engine starts a rise in voltage should be evident at just over idle.
If there is drop in voltage as engine revs, charging system isn't working. If so, disconnect leads coming from alternator to rectifier and with engine running, measure voltage(AC) across any two of the three leads. I'm not sure offhand what these Vs should be, but they should be within 1v of each other. If no or very low voltage seen across any pair, that phase is open circuit or high resistance. If this is the case (low or no V across 1 or more pairs), measure resistance across all three pairs. They should be within + or - 1/2 ohm of each other. If not, fault may lie with alternator.
If alternator checks OK for voltage and continuity, rectifier may be faulty. Disconnect all wires, check resistance across the three terminals on rect in turn, swaping probes over each time - should be high resistance one way (meg or millions of ohms), low the other (as much as kilo or thousands of ohms). If there's not a BIG difference, rectifier is faulty.
Check resistance both ways across terminal which feeds battery and earth, - should be very high (meg ohms), if low, part is faulty.
If all components check out OK and if there is enough juice to start bike, it should run OK even with flat batt.
Hope this helps.
Regards.
A.