The rules applied for the variant, where the king is captured from 2 sides are given with the version sold from the Danish National Museum. You'll find a description of these rules in English at Sten Helmfrid's. These rules tend to be used in Scandinavia.
The rules applied for the variant, where the king must be surrounded on 4 sides are found for instance at Regia Anglorum. These rules tend to be used outside Scandinavia.
Comments on the game rules.
- "Surround king from 2 sides": When you get some experience in playing hnefatafl, you will see that the game rules reconstructed by the museums (in Denmark, Norway and Sweden) are well balanced, and both sides have a fair chance of winning.
- Initial ordering: on the 11x11 board you may choose initial ordering 1 or 2. The museums state the initial ordering 1 in their folder, which comes with the game. Ordering 1 has the characteristic, that if black begins, black can block the game by occupying the squares B2, B10, J2 and J10 in the first four moves. Then in the next eight moves occupying the squares A3, C1, A9, C11, I1, K3, I11 and K9, after which the four corner squares of the board are blocked up. After this white has lost.
This is avoided by letting white move first. This problem is not found with the 9x9 board or the 11x11 initial ordering 2.
- The variant "Surround king from 4 sides": If the king must always be surrounded from 4 sides, the king will in practice always win. To regain balance in the game, special rules must weaken the king, like the king cannot participate in the capture of pieces, cannot move more than three squares at a time etc. But it surely is not very likely in a prehistoric game, that the king is weaker than his men and unarmed at that.
Notes about the king to be surrounded from all sides, the king being weaker than other pieces and the like, might show an influence from chess, which existed side by side with hnefatafl for 800 years. There are even notes from the Middle Ages, which state that the opponent must be warned before capturing the king, just as you give check in chess. Even if such chivalry might suit chess and the Middle Ages, people in prehistoric times must surely have found it hard to imagine a viking or Iron Age warrior, who shouts "Watch out!" before he attacks.