So I'm going to Germany for a semester exchange and I have a long-stay visa from Germany. Can I travel to the other Schengen states during this period with this visa or do I have to apply for a separate short stay Schengen visa?
When it comes to traveling within the Schengen area, a type D visa is equivalent to a regular residential permit. You are basically allowed to visit other Schengen countries for up to 90 days within a 6 month period.
There are some caveats - you must carry your passport or equivalent travel documents, be able to document the purpose of your visit (going on holiday should be enough), document your ability to finance the trip, be of no danger to national security or public health and not have been specifically expelled from the country you are traveling to. Since there is no immigration control on the borders between Schengen states, these requirements are in most cases rather theoretical. If however you should be checked, you probably save a lot of hassle if you have the required documentation handy.