Can I connect a computer and a printer to a switch?

Can I connect a computer and a printer to a switch?

I have a wireless router that also provides wired connections to 4 rooms in my house. I now want to connect a computer and a printer to the ethernet port in one of the rooms. can I just connect a switch to the ethernet port in that room and then connect the PC and the printer to the switch? Will other users in the house wireless or wired be able to access the printer? Will the computer connected to the switch have access to the internet?