This is my object -
This is how I want my object to look after beveling it (my professor beveled the same, or almost identical, object)
I selected the necessary edges and tried to bevel, but had no luck. Instead, what happened was another edge come up right next to the edges I selected to bevel.
Why is this? How can I get the bevel to work as needed?
Your object in your image already has the extra faces that the bevel operation would create. I've circled the square face-indicators that tell me there are faces where your pre-bevel object should only have edges. You will need to either delete them or re-create your original mesh before beveling again.
If your image was intended to only show the bad result, that's okay, too. Try resetting the Bevel tool and see the if that helps. Edit Mesh -> Bevel -> [] (Options, square) -> (in the Bevel Options dialog box) Edit ->Reset Settings. You may also want to make sure that Construction History is turned on. (It's on by default, but here's how to enable it again if you're curious:)
https://knowledge.autodesk.com/support/maya/learn-explore/caas/CloudHelp/cloudhelp/2019/ENU/Maya-Bas...
Then just try it on a default polygon cube and verify that you're getting some reasonable bevel results before trying it on your shape again.
