For wireless connection between your ADSL modem and a laptop or tablet you need a wireless router. They connect to the Ethernet of your modem and also offer wired connection for your current desktop.

So instead of modem --- PC you have modem -- router -- PC, with the modem also able to communicate wireless to the laptop to tablet. Your tablet will be able to communicate with every WiFi it finds, either your router or a wireless hotspot or a wireless router with your friends without needing anything special.