OK, so now you are saying you do not want to travel but rather to find a career that is portable. That is, something you can do while living in another country for several years or more. Whole different ballgame and much more probable.
There are of course countless paths you could take that would make that possible. So really you're back to finding a career/field that interests you because there is no use looking at something that you would hate or get bored doing after a while.
Someone could as Scuba_albany suggests become a scuba instructor but that type of 'career' only works for a while. You get too old, the only way to advance is to open your own business and that of course requires deeper roots. The thing you are trying to avoid long term. So it isn't that simple.
When I was living in Greece for a while I met some French engineers who were working on the installation of a new power plant. They spent 4 years doing the job. Project type work of that kind is common and can take you to all kinds of destinations. But it requires education and real experience to get to that level. It's also hell on relationships. Have you thought about that aspect? It's not easy to find a partner that wants to move with you every couple of years.
Trades like carpenter, plumber, electrician, etc. are quite portable. You may need to get re-certified for the country you go to but that can usually be done. If you look at Immigration websites for countries you will see what skilled trades are in demand. At one point, being a bus driver or hair dresser could get you entry to Canada for example. Nursing is in demand almost everywhere.
Nowadays, a lot of people attempt to develop an online business. If they succeed, they can obviously do that from anywhere and move if they wish. But that then presents the issue of Residence Permits/visas. You can't just decide you would like to live in X. You have to be able to live their legally beyond the normal tourist period. Not always easy to do.
The problem is daoshorizon, there ins't any magic answer and when you write, "And I can’t find many answers or advice on HOW they did it.", it sounds a bit like you are looking for one. I can tell you how I managed to be able to live without working for a living and being able to move whenever I want for as long as I want but it won't do you much good.
I took a different route. I worked in my home country, spent less than I earned, invested the difference wisely and retired in my early 40s. No need to look for a job that is portable. I don't need a job. I've lived in 5 countries in the last 22 years and I travel at least several times a year. But my route requires certain things. You have to earn in the top 10% of earners to be able to invest enough per year to reach the point where your investments will fund your life, in a reasonable amount of time. It's no use if it will take you till you are 70 to reach that goal. Not everyone is able to earn at that level obviously. It requires the skills, education, talent, knowledge or whatever to do so and few are capable of that unfortunately. I made my money in sales. Simple for me, impossible for others. If you were a major league sport player or a tv actor or a brain surgeon, you could probably do what I did. But how likely is that?
Someone like zzark takes what I would call a more conventional approach like being a plumber who moves to Spain. Only zzark teaches English. There are dime a dozen TEFL teachers who earn peanuts and there are TEFL teachers who work at the International School level and are both well paid and can move countries if they wish. They also earn enough to fund a retirement at some point in time which is something you do have to consider. You will see many people on here who are TEFLing in China or wherever but they have no real future in it. Fine for a few years but not as a long term career unless you do what it takes (education, etc.) to get up to the top ranks in that field. They think they are working and travelling. They're doing neither actually.
My point is that there is no 'HOW TO' book on this subject. You have to find your own road. Whatever way you find though, one thing is sure. It won't happen overnight.