As a slight addon to number 4 above, some bikes do not use the chassis as an earth, so you need to know this fact for your particular bike, get a service manual and read it to find this bit out.
Getting a few basic lessons to start with is the best shot, get him to show if a bulb is getting power so you can check if it a blown bulb, or something else, simple things like that.
If you want to take some cable, just get some basic figure 8, 2Amp red/black stuff. This at least should not burn out if used most anywhere, except high current circuits, like ignition and lights, but if you have a problem there, it will be beyond you.
My advice would be to take none, that way you cannot get yourself into deeper trouble with only a very basic or non existing understanding of how to fix something. Unless you are going a long way from the beaten track, there will be a motorcycle shop of some sort on your travels, and most of the Americas have bikes, not your sort, but they have bikes, and know how to fix them, so they should be able to work something out.