|Three ways of doing it.|
The cheapest and easiest is to plug the printer into one of the computers and set it up as a shared printer over the network. That requires the computer with the printer connected to be switched on for the other computer to use it.
The next way is to buy a printer change over switch. The printer is plugged in the output and each computer is plugged into the switch. You can get automatic change ever switches that switch between the two computers automatically. They operate independent of each computer.
The third way and the most expensive but the most reliable is to buy a printer server. You plug the printer into the print server and the Ethernet connection from the print server into and spare port on your router and set up the printer as a network printer on each computer.
For a home setup the first option is the most practical.
Whether you have DSL or not is irrelevant. All you need for the first option is a network connection between the two computers.
For the last option, a multi-port switch which is usually built into the router. For the second option you don't need any network hardware.