Access to this region is very easy by hitchhiking or marshrutka. Marshrutkas leave from Didube station in Tbilisi approximately every hour between 8am and 5pm. The price is 8 GEL to Gudauri or 15 GEL to Kazbegi (Stepantsminda). Though the marshrutka is quite fast and cheap, it’s always bumpy and cramped, and hitchhiking is often faster, much more comfortable, and, obviously, cheaper. Taxis are also available from Didube for about 100 GEL for a private car or 20 GEL per person to join a shared car, depending on your haggling ability.
Note that the road between Gudauri and Kazbegi often closes during snow storms and on hot spring days when wet slides are a danger to traffic, but it rarely stays closed for more than a day. Luckily, there are plenty of ski touring options on both sides of the pass, so being stuck on one side doesn’t mean you can’t ski (though, if the pass is closed, the avalanche danger may be such that you’re not skiing anyways).
There is no shortage of guesthouses along the road, and one can find an especially high concentration of guesthouses in Gudauri and Stepantsminda. Accommodation in Gudauri is significantly more expensive than anywhere else in the region, so it’s only recommended to stay there if you’re going to ski in the resort.