Doubt if you will find a copy of the copyrighted manual online. Suzuki still sells the service manual for about $60. so will not give the information away on the net. However,  it is a fairly simple system, the start button energizes magnetic switch which starts the process of energizing the decompression solenoid and then sending current to the starter motor. To make this happen the key has to be on, handle bar switch on(closed), clutch switch closed, (handle in) and kickstand switch closed if in gear. If any one of the switches do not close the process doesn't happen. It will crank w/o the decpmpression solenoid but it is harder on the starter/battery as more current has to be used and if there is a kickback, it can get expensive on pre 96 or so models. So use a voltmeter or test light (key on) or continunity testor or ohmmeter (key off),  starting at the switches make sure every one works like it is supposed to> On my B-i-L's 87 we found the decompression solenoid wasn't clean enough to work correctly so did not work, we cleaned it (the plunger and core and electrical contacts) and it works fine, I heard it click first the other day when I started it. If you search no crank/no start you will find lots of references to the the clutch switch, kickstand sw, Right handle bar switch being probelms along with many bad abttery connections on both the battery and ground wire. In DC circuits any unwanted resistance cuts the current flow and the ability of the part you want to work, to work correctly. Dirty, corroded or loose connections are unwanted resistance.  You will need a service manual (not owners) of some kind to follow the circuit and find the pieces. Max