here is the link to download the Vstar 1100 factory service manual in PDF format:
the list of possible faults for not starting is page 8-1 in the main manual (there is a supplemental manual at the end of the main manual.
The one problem with these manuals is the link/jumps in the table of contents usually dont work, so you have to page thru the manual to find the page you want.
Others have made good suggestions, here are some things to zero in on the problem quickly:
1 when you push the starter button, are there any lights on (tail light or instrument cluster lights) that you can see while you put the button? If so, do the lights dim or go out when you push the starter button? That is an indication of a bad battery, or a bad battery power or ground connection.
2 do you hear anything when you push the starter button? If you hear a relay clicking then the starter button is working, but your starter relay is either not passing power thru to the starter, or the starter is getting flakyn
3 if you push the button and lights stay on and dont dim, and nothing happens, then its the starter button, the kickstand or neutral switch locking you out, the kill switch on the right grip, corrosion on the fuse connection, your ignition switch on the key, or the relay has failed or has a bad connection. If this is the case you will need to get a volt meter and trace the wires out, and see where the 12V from the path off the battery to the starter button is being lost, or if the safety switches are showing the no-start condition.
this can be tricky, because while you are pulling on wires and checking the voltage at connectors, the wire might connect and show a good voltage. If you push the starter at that point it will start. Intermittent failures can drive you nuts trying to debug them.
Sorry if this seem nebulous, there is no single common failure that will keep the bike from starting. The service manual should help. It also has the wiring harness drawings that show where all the wires are, and there is a schematic for the electrical system near the last page of both the main manual, and the supplemental manual at the end.
One last thing, people always forget the ground connections. If you trace connectivity from the battery 12V all the way thru to the starter solenoid, and any of the ground connections in the path are corroded, the bike wont start: the ground on the relay, the ECM, the battery, the starter... The frame of the bike acts as the return "wire" - people always forget that.