Hi Kirsten,
I believe this is a Singer Class 66 sewing machine. It appears that everything is intact except for the throat plate which I think you can get on line. The bobbin can be purchased anywhere. It is a "singer class 66 bobbin and is relatively common. You just drop the bobbin in so that the thread when pulled causes the bobbin to rotate clockwise. You should be able to see a couple of little slots to pass the the thread though. It is a nice sewing machine. I have quite a collection of old Singers. I use my Singer 201 daily. It is a favorite and also uses the class 66 bobbin.
This is a drop in bobbin machine. It does not have the removable bobbin case that many machines have.
Agnes