Hotel / Hospitality Management

That is really a good question.
Let start from basic, as a fresher in the industry when you pass out from college it's really important to have national experience first with a well-reputed brand Oberoi's, Taj, ITC, because there you will learn ground reality.
Yes, working abroad is more tempting, more perks, higher pays, but first of all, you must learn basic of industry and that is best learned from your country of origin.
Depends on which country you are going settle in, if their main language is English it will be easier. If they have any other foreign language as the main language, it will be a bit difficult in starting, if you don't speak their language. Without knowing the language, it will not be easy for you to handle guest, not easy operations, maybe when you are going out you can't communicate properly.
Once you are done with language and understand their culture, it will be easier. It may take 6-12 months depending on your learning capabilities. Also, the major thing is learning the domestic culture, and not to hurt anyone's sentiment when working in some other country.

Admission to the course at various private institutes of the country is based on the candidates performance in a relevant entrance test and round of personal interview. The IHMs of the country however, follow their own admission process. All applicants are required to appear for an All-India Joint Entrance Examination conducted by NCHM (National Council for Hotel Management). Shortlisted candidates are further needed to appear for and qualify the subsequent round of interview conducted at various centers all over the country.
Candidates wishing to apply for the course need to fulfill the following minimum eligibility criteria:
10+2 level of education completed from a recognised educational Board.
English as one of the main subjects at the 10+2 level.
A minimum aggregate score of 50% at the Senior Secondary (10+2) level.