What product or gadget to buy so I can get?

[Peter H]

You could get a smartphone for Twittering or Facebooking. If you wanted a general purpose connection to the internet for a laptop you need a mobile modem, which works like a landline or cable modem but connects to the internet via a mobile account, and generally has a USB connection to the laptop.
My iPhone works both ways, with both a direct internet connection and also the ability to function as a "personal hotspot", i.e. a wireless modem that a laptop can latch onto.