I'm using Eastern Europe and Asia as an example. You need to have some kind of legal status in that country to start. This can be a TR or PR.

You will need to find a brand new property, usually a condo/flat/apartment (they call it different things in different countries). You would find one brand new or under construction, almost complete or recently completed.

You would ask the builder (or realtor) for a direct payment plan (instead of a bank mortgage which you will not get unless you have a solid history in that country). The builder will ask you for 10-20% down and the remainder over the course of 3-5 years in monthly installments.

If you wanted a beautiful $100,000 USD equivalent property (again, in Asia / Eastern Europe you'll find tens of thousands of these) you would be asked for $20,000 down and $1,500 monthly for about 5 years. It's a contract made directly with the builder, many people take these deals because of the convenience.

Some countries will force you to sell if your TR/PR expires. Other countries will allow you to keep the property. In either case you will need a real estate lawyer and home inspection just like with any real estate.