Couple different methods. This is assuming the current printer and scanner has not networking capabilities such as wireless or a NIC (Ethernet port).
My first recommendation is to buy what is called a print server. Either wireless or wired. Depends if printer/scanner will be near router. With this device you would connect the printer/scanner to the print server and the print server would then connect to the router which in return should give access to the printer/scanner to all networked computers.
Another option is if your router has a USB port and is cable of sharing a printer. Look at your router to see if it has a USB port. If it does, check the manual to see if it supports printer sharing. If it doesn't support it but it does have a USB connector you may be able to use something like DD-WRT to flash the router and enable printer sharing via USB.
Another option is to use one of your existing computers as basically a print server and have the printer hooked up to that computer. The computer would have to be on all the time but would be able to share the printer with other networked computers.