I'll assume you're asking about building an actual reconstruction of a Viking hall, not a modern house inspired by Viking stuff.

Reconstructing buildings based on archaeology is actually surprisingly easy, and has been done for at least a hundred years. The Bronze Age Swiss laketown settlements are some early examples, but for the Viking Age the house at Trelleborg was built in 1948. That one is now slightly outdated, and an updated version was built in 1985 at Fyrkat. These houses were largely inspired by the preserved ground-plan of the dug-in posts, marks of which were visible underground. So while we know the layout of the roof-bearing posts, most other stuff above-ground is not supported by the archaeology. For this, you have to make use of traditional craft experience from modern-day carpenters to find out what 'makes sense', or have to look at preserved elements from other, comparable buildings from later times (particularly the later Medieval period).

Another example are the recenrly reconstructed houses at Hedeby/Haithabu. There, much woodwork was preserved because of waterlogged conditions. One house in particular had its facade collapse, making everything fall flat under the water table and thus preserved. This allows us to reconstruct that particular house exceptionally accurately. Similarly, a place like Ribe has very good preservation, including floor levels with trash giving us hints at what activities were done in different parts of the house. A number of other places were Viking-period houses were reconstructed based on excavation are Sagnland Lejre (DK), Ribe Vikingecenter (DK), Bork Vikingehavn (DK), Årsunda (SE), Borg (N), York (UK), Historisch Openluchtmuseum Eindhoven (NL), and Archeon (NL).