The A-frame tents we use derive from the finds from the Oseberg and Gokstad burials. There were 2 tent frames in the Oseberg burial and 1 in the Gokstad. There were no finds of tent cloths which had presumably decomposed ; which perhaps needs context in that there are argument about some cloth fragments that might be from a tent. Not all of the tents are complete, however, from the primary evidence at least one of the Oseberg tents is a complete A frame with three planks at each end and a pole between them at each corner of the end triangles.
In structural design our modern A frame tents are no different to these original tents.
Guidance on making an A-frame tent is available: File:How to Make a Viking Oseberg Tent - Steve Lines.pdf.
There is also a suggestion that one of the tents could also plug into the ship deck based on notches found in the deck planks. This is quite probable but not entirely proven. In any case considering that as noted above a full tent just like we use can be assembled from the parts found, it can be assumed that the tents could be used anywhere and the deck notches are just a secondary matter intended to prevent the tent from sliding around the deck.
The Oseberg burial was dated to about 830 AD. The Gokstad ship itself was dated by dendrochronology to 890 AD so the burial was later, probably about 920 AD.
Note that this is just the frame in question, we have no period pictures or archaeological evidence of the tent cloth to be used on an A frame structure. This is where opinions start to differ because there are several ways that a tent cloth can be made to fit an A frame structure. Generally this comes down to whether the cloth is inside the end planks and tied to it, or wrapped over the end planks so that they end up inside the tent. We accept either option as authentic and acceptable, but it is recommended that the cloth should be inside the frame, because from experience it is more weathertight.
Credits: with thanks to Steve Lines.