Three roads to victory
After playing a couple of games of Settlers of Catan you will notice that there are 2 distinct paths to victory, and a possible third which walks the line between the two.
Brick and wood heavy - Settlements & Roads
The first way to victory is one where you build a lot of settlements and get the longest road. This one relies heavily on brick and wood and needs very little wheat or rock. To win using this strategy place your initial settlements such that you get a lot of brick or wood and some access to the other. Also, make sure you have plenty of space nearby to expand to. Then, start building settlements as fast as possible, pausing at some point in the middle to build one or two cities. Once you are at 6-7 victory points start making a real push for the longest road if you don't already have it. If either brick or wood are very rare in this game and you aren't on the largest supply of them, this strategy will probably not work for you. However, I have found it to be the most effective when it is possible to use.
Ore and wheat - Development cards
The next major strategy is to build a lot of cities and get the largest army. This requires that your initial two settlements are placed on good supplies of ore and wheat, ore being the more important of the two. To begin you should try to build a quick settlement either on a nearby port, or on a good spot ore/wheat/sheep nearby. Then, focus on building cities, and buy one development card almost every time you get the chance. Since getting largest army is much harder than largest road (due largely to the fact you can only play one soldier card per turn), you need to start building your army in the early game. After building one or two cities you should focus on building one more settlement. Then, stay put and focus on getting all four of your cities built and keeping largest army. If you're lucky you might even get a couple of victory points from development cards along the way. Remember, never show these until the turn on which you declare victory. This strategy will fail if you do not have good initial placement which gives you plenty of ore. Some people argue this strategy is hurt more easily by the robber. While this is true, you will have plenty of soldier cards which you can use to move it off your cities. Remember that you can play a soldier card on your turn before rolling the dice.
Mish mash
The last strategy is a mix between the above two. I find that I use the first strategy the most, and this one the next most often. The trick to this one is making sure you are always on a wide variety of resources which produce well. It grants you greater flexibility to the changing winds of the game, but its greatest weakness is it is harder to get largest army or longest road using it. It is almost necessary for you to have one of these two bonuses in order to win. So, at some point early in the game while using this strategy, you need to pick which of these two bonuses you will strive for and hold back from pouring resources into the other. This strategy works well when neither of the above two is available, but requires better skills at trading.
Okay, the above seems like a lot, but most of it is common sense and I bet you have already deduced much of it after your first couple of games. I suggest you go play a couple more games with the above tips in mind, and once you think you've got a handle on them, dive into my advanced strategy page