The answer to whether you should quit your internship is up to you. Before I got my first internship, I wasn't sure what to learn exactly, and I wasn't sure exactly how things worked in the real world. Truth be told, I actually had nightmare scenarios of sitting at a desk doing Discrete Math proofs or studying formal logic like in my Computer Science undergrad.
But the internship showed me what to study and clarified what was important. For me, it wasn't the knowledge that was so important as much as it was the skill to learn new things. The internship also gave me a reason to learn these things. For instance, I probably wouldn't have learned Visual Basic if I didn't work at my internship.
Since graduating, the side projects I've done, both paid and volunteer, have given me that focus that I needed on what to learn, because honestly, there's so much out there to learn that just picking something randomly may not always be the best choice.
With that said, you should really think about whether or not it's really worth quitting the internship if you're learning a lot there. Also, take into consideration the duration of the internship. Is it really worth breaking a commitment if the internship ends in, for example, three weeks?
Assuming you've already made up your mind and do want to quit, here's how to approach this:
- Give your internship notice that you're leaving. Two weeks should be enough.
- Explain that you've enjoyed working there and have learned a lot, and make it clear that you're interested in a possible full time position should one become available.
- Continue to show up to work and transfer any knowledge that you need to transfer over to your colleagues. Use that time to get to a stopping point on any of the projects that you're working on.
On your last day, your boss and colleagues should have everything they need from you so that there won't be any loose ends.