Playing with the Seafarers of Catan expansion should not drastically alter the strategies you were using for Settlers of Catan. The rules of the game remain largely the same, and though games will probably be longer and involve more luck, you only need to alter your decision-making slightly in order to stay competitive. Below are a few of the adjustments I suggest making to your thinking when using this expansion. If you are also playing with the Cities and Knights of Catan expansion and find that any strategies I recommend regarding it conflict with the below advice, follow the tactics for Cities and Knights.
Robbers Beat Pirates - It seems like the world is backwards in Seafarers of Catan because the single robber is a more powerful force to be reckoned with than an entire pirate ship. The ability to block other players from receiving resources is, in general, much more powerful than stopping them from moving or building ships. So, when you roll a seven or play a solder card and are unsure of which one to move, pick the robber. The exception to this is when you are competing with another player for Longest Trade Route or a particular spot on an island. In these cases it is probably worth it to use the pirate to slow your opponent down.
Gold! - One of my favorite parts of Seafarers of Catan is the new gold river tile. It is of great value, and you will be better off having a settlement (or better yet - a city) adjacent to it. However, it is commonly not worth your time and resources to build a connection all the way to such a tile. I have seen many players funnel most of their resources in a desperate gambit to get to a gold resource. Don't fall into that trap. The gold tile is definitely an asset in the game, but it also attracts the robber most of the time, and in most scenarios is not worth the extra effort it takes to reach.
Shipbuilding - With the new ability to build ships in this game, the value of wood is increased. Sheep's value is also increased, but it was already worth the least of the resources, so this doesn't account for much. Keep this in mind while doing your trading. If you can get a good supply of wood going from the early game, others who are using the ore-wheat strategy will be more likely to trade with you as they will need it in order to expand out from the beginning island. Also, the addition of ships means that it is more valuable than before to build your original settlements on the shore - something you should rarely do if playing the original game. The reason for this is a settlement/city on the shore is your only way of starting ship building and eventually expanding to other islands. If you do build initially on the shore in Seafarers, you should still only place the settlement on a 3:1 port or a 2:1 port of a resource you have easy access to.
Specific Scenario Advice - While most of the strategy advice offered so far is general and will apply to most situations, the scenarios in Seafarers of Catan will sometimes override it. For example, in the Pirate Island scenario (only provided in the 4th edition of Seafarers of Catan), the value of development cards is dramatically increased. Using the wheat-ore strategy to win is a great idea while playing it. In the scenario titled "Fog Island" ("Oceans" if you are using the 3rd edition) you should make sure to be on the cutting edge of all exploration into the sea. Not only will it sometimes give you resources back, but you will also be the first to build settlements on whatever islands you discover. In this scenario (and others where you explore much of the map) you should try to use the wood-brick path to victory. However, if you see everyone else is doing this, you could do well as the only one using the wheat-ore path. Finally, it should be noted that though many of the scenarios in Seafarers of Catan try to encourage expansion onto other islands (by offering extra victory points), don't feel forced to do so. In any scenario where you will only get a maximum of 1 victory point for expanding to remote islands, you can easily win without doing so if you have a decent setup on the main continent. Two scenarios which are examples of this are "Desert" and "New Shores". These scenarios were recently updated in the German edition to provide more incentive to expand onto islands as Klaus Teuber believes it should be a core part of Seafarers. However, these rule changes are (so far) not part of the English version.
That's all the strategy advice I can give for playing Seafarers of Catan. As always, feel free to post on the forum with any comments, questions, or suggestions. If you enjoy playing Seafarers then I highly recommend buying the 5-6 player expansion
for it. Adding more people to the game is always fun, even though it isn't fun to pay the extra $20. The expansion also includes a bunch of extra scenarios to play with 5-6 players that are great, making it especially nice to have. If you've enjoyed Seafarers and are hungry for a version of the game which relies more on strategy and less on luck then check out the Cities and Knights of Catan expansion.