Before starting the game, you must choose two locations for your starting settlements. These two decisions may seem small, but they have a huge impact on your chances to win the game. Here are some things you'll want to keep in mind when choosing where to place your initial settlements in a game of Settlers of Catan.
Each resource space has a number on it, in addition to a number of dots. The dots on each number indicate how frequently it is likely to be rolled. Consequently, you should be sure to place both of your settlements at intersections with a high number of surrounding dots. The red numbers (6 and 8) have five dots each; so obviously, you're much better off playing on an intersection of a 6, 9, and 3, than an intersection of a 4, 5, and 11.
Another thing worth paying attention to isn't just the total of dots, but the diversity of numbers you have next to your settlements. If you place your initial settlements on two 4s, two 6s, and two 9s, then unless someone rolls a 9, 6, or 4, you aren't going to get any resources -- and you should prepare for a long, boring defeat.
Diversifying your initial settlement numbers increases the chance that you will get at least something from every roll. And that's a very good thing because even if it's not the resource you wanted, you can always trade for one you do need.
Try to avoid playing both of your initial settlements in the same corner of the map, unless you can guarantee that you won't get boxed in. (And keep in mind that there are few guarantees in a multi-player game.) It may be tempting to connect your two settlements and get a head start on claiming the longest road, but more often than not this strategy won't work.
Consider building near one of the trade ports on the edge of the board. Starting on a port is probably a bad idea because you'll want your initial settlements on the intersection of three resource tiles, not only two. However, being close to a port is important, because building a few roads to connect to one early in the game will let you trade more cheaply for the resource no other player will offer you.
Pay attention to the types of materials available in the game. There are more sheep tiles than any other resource, so sheep tend to be less valuable.
The other resources have the same number of tiles -- but not necessarily the same availability! If two of the three brick spaces have low-dot numbers (like 2 and 11), there will probably be an early brick shortage as players attempt to build roads. This makes a settlement on the single high-dot brick space (a 6 or 8) a strong opening placement.
Try to have settlements that gain you compatible pairs of resources, such as wood and brick, or ore and wheat. Wood and brick will allow you to quickly build roads in the early game, working towards more settlements. Ore and wheat will allow you to upgrade your settlements into cities, thus increasing resource production.
Each of these combinations can be very strong, but if you only have brick and wheat, you can't do either of them.