Get a new alternator and reg/rec from Electrex World. Cost is about £45 for each. You can also use the Honda bodge as detailed below to replace the reg/rec and ride with your lights on all the time but the Suzuki alternators really are pants. - AC
First check it's fried - check the resistances according to the workshop manual. Check if the battery is charging up ok. Check if the alternator's ok. Remember to check the regulator/rectifier resistance the right way round ('cos there are diodes = one way resistors involved). If the conclusion is that the regulator/rectifier (henceforth known as regufier) has regufried, get yourself a Honda CX500 regufier as the replacement - apparently these almost never fail.
For my Suzi GSX400F the replacement proceeded as follows:
To access the regufier: take off fuel tank, take off chainguard, unclip the three plastic box electrical connectors under the seat to loosen things up, take off battery and metalcage (unclip bullet connectors for starter relay), take off rear plastic (the panel which has the seat lock hole it) so that you can undo bolts holding rear mudguard in place - stop rear light from falling by using a piece of string. Unscrew bolt holding rear brake fluid reservoir in place. Unscrew circlip which holds airbox with filter to the other airbox which leads to the carbs. Twist the filtered airbox out of the join (The mudguard and reservoir are in the way for this bit if you don't undo them). Twist gently so you can see the base plate on which the regufier and ignitor unit are mounted. Spanner and impact driver with cross point undoes the Suzi regufier from base plate or entire assembly (regufier + ignitor) from the air box. Suggest undo entire assembly from airbox then undo the regufier from baseplate on a desktop.
The CX500 regufier has bolt holes which match up exactly to the base plate holes with which the Suzi regufier was bolted. The CX500 regufier is much bigger though. So it needs a bit of filing away/angle grinding at edges to seat itself onto the base plate. The height of the CX500 regufier does not need filing away. It's a perfect fit.
The green fat wire from the CX regufier can be wired to where the Suzi blackandwhite wire went (to bottom of battery cage, for a ground). The red fat wire can be wired to where the red of the suzi rectifier went (plastic 4-wire box connector under seat), the three yellows can be wired to where the remaining three suzi box-connector-under-seat wires went (blueandwhite, yellow, whiteandred - these are the connections for the alternator). The order doesn't matter for the three yellow Honda wires wired up to the suzi alternator. The remaining skinny black wire is an extra connection which has no counterpart with the original suzi regufier (which had only five wires to worry about - the CX has six). This skinny black wire is a voltage sensor, and should be connected to something after the ignition switch that is always positive. I connected it up to the positive (orange) lead from the indicator relay. The indicator relay is the rubber-mounted box below the spine of the frame, below the fuel tank, and clicks when the indicators are working. It can be taken apart and adjusted with a tiny screwdriver to adjust how fast the indicators click too. Unlike the rectifiers, which have their electronics sealed in plastic and can't be taken apart. When doing the mod: Insulate, grease, insulate throughout. Crimp AND solder for best results. The mod will outlast my bike.
Wiring diagram here