During the middle ages tents were often used to house armies on the move. A variety of designs existed, and the tents of the very rich could be very luxurious indeed. Tents may be made out of wool, canvas, leather or similar durable fabrics.
Tents in the SCA
Tents are the "standard" accommodation at any large SCA camping event. At most events a mundane tent is acceptable, but cannot be set up near the period encampment, where the period style tents are located.
If you want a period style tent, often referred to as a pavilion, you may need to build your own. Other options include enlisting groups like House Woodrose to teach you how, or paying someone to build one for you.
Tents in Re-Enactment
At re-enactment events those with tents not appropriate for the time frame for the event, are required to set them up out of sight from the event. This includes canvas tents of the wrong style, e.g. a Viking tent at a 15th century event. It is unheard of for a re-enactment group of any standing in Australia, to not possess enough period tents to house a significant proportion of their membership.
There are a number of suppliers of period tents across the world, but re-enactors, especially with simple designs such as a geteld or Viking tent tend to have theirs made locally after constructing any wooden parts.