How can I get the case of my singer confidence open

If you take a look at the left hand side, the cover there (over the needle post) usually has a screw in the side which is often covered by a white disk that you can pop out by pressing on one side with a screwdriver, and another at the back that is generally not covered. It may only have one screw in the back. That cover can be removed for cleaning purposes, and you should remove it periodically to clean it. If you want to uncover more than that, generally you would remove the back first, but if you do, tape each screw next to the hole on the cover--it will save you a LOT of grief putting it back together!