Havannah strategy has evolved over the years. As I write this, winter solstice 2016, my rating at Little Golem is 1929 whereas the highest ranked player rates 2377. That should tell you enough about the game and my ability, or lack thereof, to comment on strategy. This is merely about basics.

A very basic property of Havannah is this: of all games that can end in a draw, it must have one of the smallest margins.
It's easy to construct a drawn position, but in thirty years of play, there has been only one recorded base-8 draw.
There are two immediate consequences:

• The first player to complete a ring, bridge or fork, is the winner, so white has a first move advantage, and it is not diminished by a drawing margin.
• Since a draw is no option, a sound defensive strategy will eventually turn into an attack all by itself!

To balance the first move advantage Havannah uses the swap rule.
The second property was not immediately obvious in the first year of the game's existence, when it was extensively played at the University of Twente and its games club 'Fanatic'.
It took Roelof Moll, a local Chess player who had played only for a couple of months, to point it out. He started winning consistently by following his Chess instinct and taking the center. He didn't care for speed, he cared for safety.
His reasoning was that it doesn't matter how 'fast' a group threatens to connect, if it's dead or forced to go roundabouts.
Cutting the opponent's groups from above (that is: from the center) limiting their options to at most two sides and one corner, he proved that all our previous strategies were in dire need of reconsideration. From his contribution came the concepts of snake strategy, with the emphasis on speed, and spider strategy, with the emphasis on safety.
It gave rise to the Safety Speed Dilemma, illustrated here in a nutshell, but actually pervading Havannah in all strategical and tactical aspects.

White 1 brings the intended connection one step closer, but isn't save: black can cut with 2. White 3 is safe: barring a simultaneous ringthreat, black cannot cut. But white has not gained any tempo: he still needs two moves to connect. From this example an inductive understanding may already emerge that safety and speed tend to follow different routes! This principle pervades Havannah from the very basic tactics shown, to the intuitive realms of opening strategy.

A frame
The main strategic goal in Havannah is is the establishment of a frame, a connection aiming at a ring, bridge or fork, that, though still incomplete, cannot be broken by the opponent. With safety taken care of, it gives rise to two simple strategic truths:

• Attacking a frame pushes it right into victory! The only defense is: having a faster frame, or at least threatening a faster connection in the process of making one. This may seem quite obvious, but even experienced players do not always recognize a frame until they discover that their attempts to cut or block were in fact counterproductive and would better have been left undone. In short: only defend if it can be defended and only cut when it can be cut.
• Balanced games, that is: games that are not decided by tactical oversight, will eventually take the character of a race. Assuming that both players eventually frame, both will engage in the difficult process of counting. The faster player will make it a race without bothering about the opponent other than to answer local tactical threats.