This probably varies a bit by country, but IMO, it's not easy. My opinion is based on limited statistics from people that I went to school with, friends, acquaintances and hearsay.
Let me recall an anecdote - this is from India. I had gained admission into a Graduate Program in the US, and was standing in line at the Consular Office, waiting for my visa interview with the agent behind the window.
The person in front of me was being interviewed: he had just been accepted by the New Jersey Institute of Technology for (I think) an MS in Computer Science. The agent asked the applicant to explain why he believed he would get a top-notch education at this particular Institute, and why couldn't get a similar education in India. The applicant couldn't sufficiently convince the agent (he could not/would not, for instance, state how high the NJIT Comp Sci program was ranked among others). His student visa application was denied.
More or less simultaneously, another person was being "interviewed" (I would say 'harassed') at the next line over. Whenever the agent asked this person a question, he began by prefacing his response with a "yes", and then proceeding to answer the actual question. This is not uncommon among Indians - the almost involuntary utterance of the "yes" is essentially an acknowledgment that the question has been understood. The immigration agent appeared to find this extremely annoying. After the first question was answered in this manner, the agent cut off the responder at the beginning of his next response with: "What do you mean by "yes"? How is "yes" an answer to (insert question here)?" When this happened a third time, it quickly devolved into the agent yelling at the applicant, and insulting his language and comprehension skills (loudly enough that the couple of hundred people in the office could all hear it) before rejecting his visa application.
So not only is it important to have the required academic/professional qualifications, you also have to get a little lucky and not end up on the other side of the window from a pompous immigration agent who can't stand having to live in the squalor of a third world country and believes s/he is doing you a personal favor by granting you a visa.