A non-Israeli resident living in Israel for more than two years without a suitable visa starts to lose his future Aliyah Benefits.
Check here how to avoid losing your future Oleh Chadash benefits while living in Israel.
You can apply for a 1-year Student Visa through Misrad HaPnim. Check here how to do it.
If you are eligible to make Aliyah but you are not sure whether it is the right choice for you, a temporary residency (A1 visa) might be a good alternative. Find more information here.
If you are making Aliyah from within Israel, you are basically changing your status from a tourist to an Oleh Chadash. This procedure is different from making Aliyah from abroad, so if you are already in Israel and want to make Aliyah, follow the instructions here.