Going on a student mobility can be a very fun, educational as well as a cultural event. However, in order to be successful in international student exchange, then it is essential to choose the right mode of mobility as a student. If you are a student who is studying in a European University, then you will need to apply to Erasmus programs which are specially designed for European students to study at another European University, Usually all European students will use the ECTS Credit Transfer system, so this makes it easier for many European students to study at another European university and get the necessary credits transferred without any hassle.
If you are from a non-European country, then you will need to apply for student exchange through a bilateral agreement between your university and its partner university, For this to happen, you will need to go to your international student office at your home university and you will need to submit your application to your international office for student mobility consideration. There may be some GPA requirements at your home university, so you should inquire about these requirements before applying. If your application is successful, then your home university will nominate your application to its partner university. Once the partner university accepts your application then Waala, you are ready to go to your student exchange program at another country.
In general, student mobility is always free of charge as you only pay the tuition fee to your home university unless you are going for a double degree program in which case it will be chargeable for both home university and the partner university. As an exchange student, you will be responsible for accommodation costs, though there may be subsidies and scholarships available depending on the country.
As another alternative, you may be able to apply to international organizations such as ISEP in USA, which can help you to apply to their network members, though there may be some charges involved for the application process.