I'm an American who has lived abroad for more than half my adult life. We could dedicate a whole forum to expat investing. That said, there are some basic rules.
1) Broadly speaking, expats come in two stripes: those who just take off to somewhere they like, live cheap, and get low paying jobs like teaching english. It can be a great experience, especially if you learn a language. Some parlay their experience to startiing a business abroad (difficult). Then there are expats like myself: those hired in their home country, sent overseas on an expat package which includes luxury housing, freight allowance, school allowance if you have kids, and pay differentials. It's getting harder to get this type of job but they're still around.
2) Your goals should depend on which group you're in. If your in teaching English, you probably aren't saving much if anything, but learning a foreign language could be invaluable. Ditto for the experience you get surviving in another culture.
3) No matter how long you stay "out", you gotta have a home base. Real estate back home is a great investment. Buy a rental property, get a property manager in place and lease it out. You get the income (hopefully enough to pay your mortgage) plus you get a place to hang your hat if/when you decide to return home.
4) Keep things like your driver's license, voter registration, etc. current. A lot of expats don't do this then have to scramble when they decide to go back especially if they want to get a mortgage. File a tax return, even if you owe no taxes -- this is a great way to prove residency somewhere (at least in the USA).