What is the process to apply for A Canadian work visa (since it is a paid internship)?
Normally, the prospective employer would have to take an active role to sponsor the prospective employee. Information for prospective employers is available at the Canadian government page Hire foreign workers. More general information, including information for prospective work visa applicants, may be found at Work in Canada.
Can I apply on his behalf in the original country of residence?
Perhaps; there is a form (pdf) available for him to authorize a representative to act on his behalf.
The usual expectation is that applicants will submit their own applications in their country of current residence. As an international student in the US, your friend should apply in the US. To explain why, consider that part of evaluating the application will be examining your friend's school records. A consulate in the United States will be in a much better position to do that than will a consulate in your friend's country of origin.
If your friend will be in his country of origin during the application process, then perhaps he can apply there, but he would probably not need your help for that. The portions of the application process that do not require a visit to the consulate can be processed online.