Usually, you need a presence in each country, like an official entity. It's easy for a myriad of countries to do that for a fee; even in Dubai, you can form a company. Then you can acquire numbers easily in these countries. I am now supporting the UK (easy to get)/US/CA, and will soon support some European countries as well. What's hard are the countries that require authority talks like Egypt :D

I am Egyptian living in Europe, so I want to support it, but I left it for a bit.

There are a lot of telephony providers out there (Twilio, Bandwidth, etc.) So it's easy to start building.