Starter solenoid connections

I'm assuming it was a new starter motor not a second hand unit. Not all 'new' batteries are fully charged when you buy them so if you have a charger put the battery on charge overnight to make sure it is at it's max. Next turn everything else OFF before you start the bike. Each thing you turn on like the lights takes power away from the battery. features like the lights and fuel pump don't use a lot of battery power but a starter does.
With a multimeter set to DC Volts check for power supply to the starter itself and to the Solenoid that triggers the starter motor. You should get somewhere around 12.6 volts. Does the bike start if you 'jump' the solenoid? (a thick INSULATED wire or an INSULATED screwdriver across the large terminals of the solenoid).
You could check if the actual engine turns to make sure it isn't seized. First put the bike on it's centre stand NOT the side stand as you will need the rear wheel off the ground to do this. Get a helper to gently lean on the handlebars to keep the rear wheel clear of the ground. With the engine OFF, with the key OUT and the bike in neutral, keep well clear of the chain and rear sprocket (toothed cog). Roll the wheel by hand. It should spin freely with just the sound of the chain quietly clicking and possibly a quiet 'hiss' from the rear brake. Put the bike into gear, 2nd or 3rd if you can. Try to roll the rear wheel by hand. You will get resistance but it should turn. You should get regular spots of resistance (compression stroke) and free rolling (exhaust stroke). Roll the wheel through 4 or 5 full turns to make sure it doesn't lock up part of the way round.
Buying a non-runner is always a roll of the dice. Sometimes you inherit someone elses mechanical headaches.

Check the light switch , wiring circuit for broken wires ,loose connection or corrosion or even a blown headlight bulb .

there should be a plug that is on the end of the wires?? Google Make & model & ask for wiring diagram

A starter freeze-up would probably give forth much smoke from the wiring and the starter motor itself. You need a test light or meter to check for power at the starer solenoid. Check from ground (engine block) to the terminal that connects to the positive battery cable (should light). If nothing, check the battery terminals for corrosion (use a special battery cleaning brush from your auto parts store --cheap) and check the cables near the terminals for excess wire corrosion. Recheck for power at the solenoid again--it should now give light (meter read 12.6 volts). Try the starter again--if only hear a 'click', test at the starter motor terminal for power when the key is turned. If you get light, then the starter motor is defective (likely a bad brush or spring) and should be removed for repair or replacement. If you got no power at the starter terminal, then replace the solenoid. Hope this helps!

replace the starter solenoid relay.

Starter motor bearings or brushes are sticking. Strip and overhaul.