How to ask for an academic agreement with a foreign faculty? In my current place of work we would like to offer our students the possibility to follow courses and do research in foreign universities, but I am a little bit dubious how our faculty would manage to do that. I mean, what is the procedure to follow to make this kind of academic agreements? Should one write directly to the Dean of the objective faculty of which we want to make the academic agreement? What would be catchy for them to agree to have an academic cooperation with us (related to exchange of students and lecturers for short periods of time)?
Setting up a formal relationship between departments can be a lot of work, and requires strong motivation on both sides.  

A possible lighter-weight option to consider would be a more unidirectional program like exists at the department of one of my colleagues in Europe.  In his institution's Ph.D. program, each student is required to do two terms abroad at another institution.  The university supports this by continuing to support the students financially while they are abroad, but it is up to each student and faculty member to arrange where they go and who they work with independently.

As I have observed it in practice (i.e., being on the other end hosting a visiting student), this it much easier for others to agree to than a formal arrangement between faculties, because it requires fairly little investment and are likely to be covered by normal "visiting scholar / visiting student" arrangements.  It's also a great way to bootstrap collaboration with a foreign colleague.