Three operators cover the country: Magti, Silknet and Cellfie. All three sell prepaid tourist bundles at the airport, and all three have shops on every second block in Tbilisi.
What you need: your passport. Registration is done in the shop and takes a few minutes.
What to watch for: the airport bundles are priced for tourists. If you are staying, walk into a city shop the next day and ask for a monthly plan instead — it is usually a fraction of the same data.
Coverage is strong in the cities and along the main roads, and thin in the high mountains. Download offline maps before Tusheti or Svaneti.