Probably the most common and well-documented variant of Hnefatafl, what we know of Tablut comes mostly from the diary of Carl von Linnaeus (later, Carl von Linné), who traveled among the Saami, an aboriginal population scattered throughout several Scandinavian nations, in the 1730s. He recorded his observations of several games of Tablut, but as he did not understand the Saami language, the rules as we know them are based on deduction.
The Tablut board is 9x9, and the defenders are referred to as Swedes, and the attackers as Muscovites (or Russians). The following diagram shows the starting layout of the board, with the * symbols representing the Muscovites and the @ symbols being the Swedes. The K is the king.
-------------------
| - - - * * * - - - |
| - - - - * - - - - |
| - - - - @ - - - - |
| * - - - @ - - - * |
| * * @ @ K @ @ * * |
| * - - - @ - - - * |
| - - - - @ - - - - |
| - - - - * - - - - |
| - - - * * * - - - |
-------------------
While similar to Hnefatafl, the rules of Tablut have several major differences. Please refer to the Hnefatafl write-up for the core rules of tafl games. The first thing you may notice is the absence of the four king's squares, which are normally located one in each corner and serve as the escape routes for the king. In Tablut, the king may escape by reaching any square along the edge of the board. This may sound far too easy, and indeed for many years this game was written off for that very reason. However, a later re-examination of Linnaeus' diary indicates a stipulation that was originally overlooked.
The areas in which the Muscovites begin the game, referred to as the "base camps", are restricted areas with special properties like the central king's square. The Muscovite pieces may move around within the confines of these base camps, but once a piece has left the camp, it may not return, nor may it pass over any base camp square during a normal move. These rules also apply to the Swedes, who may not enter or pass through the base camp squares at any time. Likewise, once the king has left the central king's square, he may not return to it, nor may he or any piece pass over it. This differs from regular Hnefatafl, in which the central square may be re-occupied by the king, and any piece may pass over it during a normal move.
There is also an additional capture possibility for the Muscovites in Tablut: if the king and an adjacent warrior are surrounded in a combined trap, the warrior piece is captured (although the king is not). This rule is easier to illustrate than to describe, and is shown in the following diagrams:
| - * - - | - * - - - - * - -
| % K @ * | * K @ * - % K @ *
| % % - - | - * - - - - * - -
| % - - - | - - - - - - - - -
As you can see, the king must be surrounded on three sides by Muscovites and/or hostile squares (indicated in the examples by % symbols), and on the fourth side by one of his own warriors. An opposing Muscovite must then sandwich that warrior between himself and the king, which results in the Swedish warrior's capture.
Another rule evolved presumably as a response to chess' convention of announcing "check" and "checkmate". When the king has a clear avenue of escape to the side of the board, the Swedish player must say "raicki". If the king has two clear avenues of escape, he must say "tuicku". This is the equivalent of checkmate, as the Muscovite player will only be able to block one of the two escape routes on his next turn. I am unsure of the exact translations of these words, but modern rules of Tablut require the Swedish player to say something along the lines of "watch the king", so that may be the approximate meaning of "raicki".
Tactics for Tablut differ from Hnefatafl primarily because of the strategic importance of the base camps. These are a great asset to the Muscovite player, and should be used to every advantage. As mentioned in my Hnefatafl write-up, one of the most effective tactics for the attacker is to hem in the defending player with diagonal lines, as these cannot be breached once established. The base camps provide an excellent assistant here, as they free up pieces that would otherwise be required to seal the edges of the board. Only two Muscovite warriors are thus required to seal any one corner of the board.
The chief advantage to the Swedish player is the simple fact that he now has sixteen possible escape routes instead of the four provided by basic Hnefatafl. Even with the base camps, the Swedish player needs a minimum of only four moves to reach the edge of the board and escape. Some consider this an imbalancing advantage, and as a result it is not uncommon for the king in Tablut to be declared "unarmed", which means he cannot be used to capture Muscovite pieces. Even so, the best tactic for the Swede is to open up the board and let his king out, forcing the Muscovite player to scramble in an attempt to cover all possible escape routes.
In general, beginning Tablut players should start as the Swedes until they've learned the game, at which time they may enjoy the more challenging aspects of the Muscovites.