Unless you are getting two ip addresses from the dsl modem you MUST use a router. A router will enable more than one computer on a network to access the internet at one time by using DHCP to hand out ip addressess for the new network, called NATzZ. A switch just directs packets to the right computer.
Most routers you buy at electronic/computer stores have a built in switch to allow more than one computer to hook up to the router. Normal routers usually only have 1 port on them.
DSL modem -->Router/switch combo--> computers.