We advise you to start familiarizing yourself with the visa procedures for the relevant country at an early stage, in order to to get all the required documents in time. The partner university will often give useful advise on the student visa application process in their country, but you are responsible for applying for the visa. You may want to contact the relevant embassy for detailed information about the process.
A visa application can include one or more of the following: an application form, an acceptance letter from the partner university, an ID photo, proof of health, proof of insurance, proof of financial means, criminal records, birth certificate. (This is not a complete list, and you must check what is applicable for your exchange destination).