What are some steps to take for someone planning on moving outside of the U.S.?

First step.

The worlds 200 other countries do not care much what YOU WANT.

BANKS have been exchanging currencies for CENTURIES. Easy process. You sell yours and buy the other one. The money changer takes a commission (Fee) for the trade.

It is up to you to provide reasons this other place MIGHT want you to move in.

A visa application is similar to a job application. You show why YOU are better than the others trying for the same thing.

For example a needed job skill.

Military does have some very useful after service possibilities a country MIGHT need.

A tank mechanic can repair large vehicles. A grenade tosser maybe can pitch baseball.

MOST places expect you to be about age 25 with related education and work experience at a very high level. A BILLION others on the planet want to move too. YOU have to be better than about 90% of the other applicants.

Things like a Masters Degree or PHD helps.

For Young people suggest you explore the world of a work holiday visa. A year or two at some distant place. You work a bit and explore . After your time is up on to the next country. You will not have a pocket full of money but will get lots of time to explore. There are five countries that offer working holiday visas for U.S. citizens: Singapore, New Zealand, Australia, South Korea, and Ireland.

The days of wandering the planet at will was last century.It can still be done but is not easy.

Living and working in another country isn't easy. You generally need a visa that allows you to live and work in the other country and that usually requires that you have a job already lined up in that country. Check the consulate/embassy websites of countries you're interested in for requirements for a visa. Many countries require that you have special skills, education or experience that cannot easily be duplicated in country to work there. When my job was transferred to Italy, it took about 8 months to get the paperwork and get approved to get a visa. You should also check the expat sites for that country for information/advice.

You will be dealing in the local currency which isn't a problem with currency exchanges and banks. One issue that you may not be aware of is that you will have to file tax returns in the US and your host country which can be expensive. If you can swing it, living in another country can be a great experience.

What a great idea..join the army, go overseas, meet interesting people...and shoot them...

You can't move anywhere without a visa. 

You can convert USD to other currencies easily. 

If you live in another country and you have money in the US, you can open a bank account in the country where you live and have your US bank transfer the money. When it arrives in that country it will probably be automatically converted to the currency of that country. Or not, as you wish, though if you want to take some of that money out as cash then you had better get it in the currency of the country where you wish to spend it. In many countries you can have bank accounts with different currencies in them. Here in Canada, for instance, the major banks have accounts in which a Canadian can hold US currency.

Currency exchanges are business that buy and sell money. If you go to one with some US cash, they will exchange it for the cash of another country. Most large airports have a currency exchange right there in the airport. Most banks can also change currency, though unless it's a very large bank you might need to let them know in advance what currency you want to change your cash into, as most banks don't keep a lot of different currencies on hand.

As for how you can live in another country and be well off and not have to worry about finances, well, it's the same as it is in the US. Have or earn a lot of money.

Most countries have currency exchange retailers, where such exchanges can be made.

Your first issue in moving to another country is to qualify to be granted the privilege to move there.