I am glad you are interested in International business and working internationally. I have been fortunate to lived and work in several countries - Canada, US, Japan, Philippines, China and Hong Kong. There are several paths to international business careers.
1. you can work in the US for an international company and your job responsibilities can require you to travel to various countries to fulfill your work
2. you can join a company that requires you to work internationally. These jobs are less frequent and often you have to make your intentions clear at the outset and demonstrate that you are the right person to work internationally. Because it is extremely expensive to send people overseas to work (typically 3-6 times that person local cost because of taxes, housing, home leaves, children education, etc), then you need to demonstrate you bring more to the table with skills and contributions, and that the company sees a longer term potential in you so the assignment can be developmental as well.
3. join a company in the international market. This option will require you to speak the local language and be prepared to live in the local lifestyle since you will be paid as a local employee. Great experience that you can leverage for future career opportunities.
I would say it depends on the country also on your experience and skills among other things. Generally countries such as India, China or Brazil take it for granted it will be highly competitive simply because of the high number of graduates excellent business schools and younger workforce.