The New England reenactment group Hurstwic, which concerns itself exclusively with Viking age Scandinavia, has helpfully provided us with a list of things that are known about the game, which I quote here:
The most complete descriptions of the game in the sagas are: Grettis saga (Gr.s.) chapter 15; Gísla saga (G.s.) chapters 15 and 18; Egils saga (E.s.) chapter 40, and Eyrbyggja saga (Ey.s.) chapter 43. From these sources, we conclude:
The bat was such that it could broken in anger, and that it could be mended on the spot (G.s. ch18). The word used in the stories is tré, meaning tree, but used for many wooden objects. However, in one instance (Gr.s. ch15), the word used is knattgildra, which has the sense of "ball catch" or "ball trap". Perhaps the bat had some element or elements that allowed it to catch or hold or carry the ball.
The ball was hard enough that when thrown in anger at another player, it could cause a bleeding injury (Gr.s. ch15). And if thrown with enough force, it could knock over another player (G.s. ch15). Loose balls bounced a long way over the ice (Gr.s. ch15).
The playing field was usually near a pond. [...] Some modern scholars have suggested that the game was played on the surface of a frozen pond. Ice certainly figures prominently in the stories (G.s. ch18, Gr.s. ch15). Gull-Þóris saga (chapter 2) specifically states the game was played on the ice at Berufjörður (á Berufjarðarísi), and Þórðar saga hreðu (ch.3) says that games were played on the ice at Miðfjörður (á Miðfjarðarísi) between the farms of Reykir and Óss because the fjord froze easily there. (That location might be more accurately described as the estuary where the river meets the fjord.) [...]
Later in the saga (G.s. ch18), games were held at Seftjörn in the winter. Þorsteinn brought Börkur down on the ice. However, the "ice" is actually svell, a word that implies uneven or lumpy ice and is usually applied to ice that has formed on land, rather than over a body of water. [...]
Egill, a slave, was given instructions to go to the games festival and kill one of the Breiðavík men. Egill waited in the mountain pass above the games field where he could see the activities at the festival. When the cooking fires were lit, and smoke obscured the pass, Egill went down to cooking sheds to complete his assignment. However, before he could kill anyone, he tripped over his shoelace and was captured. [...]
However, the games festival was held on Winter Nights (veturnætur), the beginning of the winter in the Norse calendar. This was a time for sacrifices, game festivals, and weddings, and it occurred in mid-October.
In October, the mean temperature in that part of Iceland is above freezing, so it seems unlikely that ice had formed on the ponds. [...]
The games were viewed by many spectators (G.s.ch18). [...]
Games could last for days (Ey.s. ch.43), although one day games are also mentioned (Gr.s. ch15).
Players were divided into two teams (Gr.s. ch15). English translations suggest that players were lined up with opposing players facing each other, although I wonder if that's reading more information into the original than is really there ("Síðan var skipað mönnum til leiks.", Gr.s. ch15). There is the sense that certain players on one side played against certain other players on the opposing team (G.s. ch18, E.s. ch40). Players were matched on the basis of strength (Ey.s. ch.43, G.s. ch18).
The play involved hitting the ball, catching the ball, and running with the ball while opposing players chased the runner (Gr.s. ch15). When the ball was hit, it traveled through the air, rather than on the ground (Gr.s. ch15). Players were held and tackled while the ball was in play (G.s. ch15). During the game, the ball could go out of play (G.s. ch15).
This isn't a lot to go on. It leaves room for debate even about the nature of the surface on which the game was played (I tend to presume the references to svell are the most reliable answer, and that it was likely played on frozen fields), and what the rules were like is never specified even in the broadest of language.
I know of three hypotheses about the relationship between knattleikr and other, more familiar games. One posits that it is part of the football family, perhaps even a missing link between football-like games and hockey-like games (which do seem to be distant relatives, with both likely deriving from the Roman game of harpastrum); this is the presumption which seems to underlie Hurstwic's reconstruction of the sport. Another holds that it is a distant relative of baseball; certainly the Protoball Project mentions it as an early bat-and-ball game of the sort that develops into the safe haven games we know today. Finally, I have read a reconstructed set of rules for the game which proposes it is related neither to these families nor to any other sport familiar from non-Scandinavian sources.
The last of these hypotheses appears to be based on trying to come up with something that matches as many incidental details as possible, without reference to any sources other than historic mentions of knattleikr. This leads to positing a game in which players each compete against a single player from the opposing team, with the possibility (sometimes suggested as a likelihood) that there were as many balls in play as there were players on each team. This seems a mistake, but if we do not suppose that the lining up in opposed pairs is so strong a feature, we're left with nothing on which to hang a hypothesis.
The notion that knattleikr is an ancestral form of safe-haven game seems improbable, given that it seems each player carried a staff or bat, rather than only one at a time; further, safe-haven games do not involve both teams lining up at once. (They do often involve a line for the batting order, but the other team is at that time scattered across the field.) Safe-haven games also do not allow for tackling of those who are carrying the ball. While it is certainly possible to design a safe-haven relative which avoids these problems (and if anyone does, I would very much love to play it), it seems unlikely that one of the earliest games of the family (most probably the very earliest one known, if we accept this hypothesis) would be so wildly different from all other examples.
The presumption that knattleikr plays a lot like rugby is a promising one, seductive for the would-be reconstructor. The opposing lineups suddenly come to sound a lot like the opposing formations in which teams in other football-like games form up, rather than strict lines a la red rover. Indeed, from a rules standpoint, there's only one big question for which plausible answers aren't forthcoming - if the ball can be carried (as it clearly can), what are the sticks for? They aren't used in the manner of hockey or hurley, and it seems somewhat unlikely that they were used to transport the ball as in modern lacrosse (although that's not out of the question). The best answer is to suppose that knattleikr marks a transition from the Roman stickless football games, a family which persisted in Romance-speaking areas for many centuries thereafter, and the hockey-like games of the Celtic fringe. This, however, implies that the stick games were then introduced into the Celtic-speaking areas by Vikings or their descendants - not an implausible suggestion, but one for which I am unaware of any evidence. Hurstwic embraces this notion, at least tacitly, and so posits that the point of the sticks is to impede your opponents, effectively playing rugby with stick-checks, though they do also include a rule about striking the ball with the sticks as part of how each play is started.
Since it is so hard to come up with a reasonable reconstruction of an isolated knattleikr, I consider the football-like reconstruction as played by Hurstwic to be the most plausible interpretation I have yet heard, though I assign it a far lower probability of being accurate than what I would assign to the likelihood that it was a game unique enough to be beyond our grasp today. Nonetheless, in organizing a knattleikr game at a medieval event in February, I plan to use the Hurstwic rules, for lack of anything better. I'm billing it as being like "Viking rugby" for the sake of those who find the Old Norse name too much of a mouthful, but this nickname inherently implies acceptance of the assumptions that underlie the Hurstwic version of the game.