RE: How do you make an income while you are traveling?
There are some countries where you can get a Working Holiday Visa which will allow to stay in the country for up to 12 months and do some unskilled jobs, Australia and New Zealand are two countries which offer these.
It seems you’re from the US, and have asked this question in the Europe section, so I guess Europe is where you really want to go. While the US might have Working Holiday Visa arrangements with some European countries, you will need to do some research and go to each country’s Embassy website to find out if this is possible. Otherwise, it’s not possible for an US citizen to go to Europe and just pick up odd jobs.
Also be aware that much of Europe is part of the Schengen Zone (all of Western Europe except UK) and as an US citizen you can only stay in this part of Europe for a total of 90 days out of every 180 days.
Suggest you start doing your research now, also get a part-time job and save like mad, then when you turn 18 you’ll have a good idea of where you want to go and what you’re allowed to do.