As a general note, this guide attempts to stay away from sweeping generalizations of what strategy or tactic is "best". There is seldom a best strategy or tactic (such as "always build a city if x happens, or a settlement if y happens"). Instead, I try to represent each concept as a series of choices to be made, and the advantages and disadvantages of each. Settlers has too many factors (many beyond your control) to come up with some sort of formula to win in every situation. Instead, you need to be flexible and adapt as the game progresses. Don't be afraid to try out new strategies, as you may need them someday.
This guide assumes you have only the Kosmos (German version) or Mayfair (US version) Basic set. Many discussions also refer to elements of the 5-6 Player Expansion set, and the Kosmos Seefahrers / Mayfair Seafarers expansion set (referred to as "Seefahrers" in this guide). These two expansions, while adding some new game elements and rules, do not substantially change the overall game mechanics. Later editions will address the Stadt and Ritter Expansion in a separate section, as it in essence creates a new game.
The initial setup should take into account a number of factors. Note that a lot of the information below is also applicable whenever a new settlement is built.
1) Production Value
Before you place settlements, figure out how much the intersection will produce. First, a refresher on the number distribution of two six-sided dice, for those of you unfamiliar with the bell curve. Below is the number of times (out of 36) that a particular number shows up:
So if you have a settlement on a 3/5/10 intersection, the chance that it will produce something that turn will be 2/36 (the chance a three will be rolled) + 4/36 (the chance for the five) + 3/36 (the chance for the ten), or 9 out of 36 in total. The ranking for this intersection, then, is 9. Any intersection can be ranked on just production value from zero (the edge of a desert on the water) to 15 (the intersection of three hexes having an 8 or a 6). Note that an intersection ranked 14 or 15 is not supposed to happen in the basic game (as an 8 or 6 hex should not occur next to each other), so the effective range is zero to 13. The intersection with the highest rank should get you more resources.
On some newer Mayfair versions of the game (3rd edition - colonial art), the number tiles have from one to five little circles on them, giving you the odds out of 36 that number will be rolled. Just add them up to get the rank.
Don't have the new Mayfair edition, but want an easy way to remember how to rank an intersection? For each number tile surrounding the intersection, figure out the difference between that number and seven. Add them up, and subtract the total from 18.
The rank of the intersections on which you place your first settlements is (in my opinion) the most important factor to consider in the initial setup. The other factors below should be considered only after figuring out how much they will decrease your overall production value, and if it is worth it.
2) Strategy you will use
Of course, a straight production value is less useful (maybe a LOT less useful) if you are not getting the combination of resources you need.
3) Six and eight hexes
Don't just automatically place on a six or an eight hex because it has the highest production value, or because those chits are marked in red. Just because that particular hex has a good production value does not mean the overall intersection does too. Look at the rankings for all the good intersections. If two intersections both have the same ranking (for example a 6/10/4 intersection and a 5/9/4 intersection, both ranked at 11), consider the one without the six or eight.
Why? Sixes and eight's can be big liabilities. First, the robber is particularly drawn to sixes and eight's, no surprise here. Second, as sixes and eight's attract more people, it will be more crowded and harder to expand around them. Third, if a hex around one of your intersections without the six or eight draws the robber, it will do less damage, as it will have to be put on a hex with lesser production capability. In general, sixes and eight's are best for people who plan to draw a lot of cards, so you can have some knights ready to move the robber off.
A settlement with an intersection with one good number and two bad numbers will be practically useless when the robber is placed on the good number. (Isaac Kuo
A big decision is where to place a second settlement on a hex. If there is only one settlement already on a hex, you usually have a choice: build at the opposite corner (blocking the hex off from any future settlement), or build two away from the first settlement, leaving a third location open on that hex. What you decide is a major factor on whether the robber visits you or not.
Blocking off a hex could be an advantage if you can restrict that resource to other players (this can be a substantial advantage on a rare resource, or a resource that everyone needs for their particular strategy). A disadvantage is that you decrease your own expansion potential. Potentially a bigger disadvantage is that you will appear to create a monopoly, and draw the robber (see problems with this in the Overall Strategies section above). Because of the problem of the robber showing up more on a hex in your sole control, if you block off a hex you should seriously consider doing it only on hexes where another player has the first settlement.
Try not to place both settlements around a single good producing spot. Besides probably reducing expansion capability, this makes that spot a prime target for the robber. (Isaac Kuo
If there are two different players already on a hex, and a third position is open, seriously consider building there. It is very hard for the robber to stay on a hex with three players who all want him off. And fewer players will place a robber there in the first place.
5) Other players
If you place first and put your first settlement on that great eight Ore hex, don't depend on that six Wheat hex being available when you place your second settlement. When going first, your strategy might have to be more flexible as everyone will be placing all the rest of their settlements before you. In this case, you may not be able to figure out your strategy until you actually place your second settlement. (Isaac Kuo
Other players also determine your expansion capability. Make sure you are not cut off from future ports or other resources you might need, or from being able to expand. (Isaac Kuo
Don't place your initial settlements just to screw other players. I read one guide where the author said the first settlement is for optimizing production, and the second to hurt other players (grabbing a port s/he needs, etc.). Remember, your goal is not to have a particular player lose, it is to have you win. You are not going to win by sacrificing your production to hurt someone else. Maybe the other person(s) you target will lose too, but you will fall on the sword to get it done, and probably wind up letting a third person win (who presumably focused on a placement for optimal production in the beginning and was ahead of you both). If you can place a settlement and screw someone at the same time, then great, go for it. A much better strategy is to convince someone else to screw the first player. This is not to say you shouldn't work against other players, but don't start the race with a broken leg (note to self: enough with the metaphors already).
6) Distribution of numbers
Two hexes each with a five will produce the same number of resources on the average as two hexes with a four and a six. However, the distribution will be different. Settlements on a smaller selection of numbers mean that you will get a lot of resources clumped together, while settlements on a larger selection of numbers means that you will get resources spread out more. Both have their advantages and disadvantages.
The same number on two resources that are commonly used together (for example, wood and clay) can be very useful, as they can immediately be used and less port trading will be required (Isaac Kuo)
Also, consider placing your settlements/cities on numbers so production matches your ports. For example, if you use a 2:1 port, having two settlements or two cities on a hex for that resource will allow you to trade more easily. This also means that if you have a 2:1 port for a resource, you don't necessarily need a settlement and a city on the same hex as you will produce three of that resource (unless you need one of that resource itself). (David Grabiner
Decide to where you want to build. New people playing the game usually place their roads towards high value hexes, and then kick themselves because they are taken before they get there, and as it is usually so crowded around high value hexes they have no where else to go and they wind up building in the opposite direction. If you want to be more sure, build towards the sea, and ports. Not too many people start there, you will need a port, and you may be able to pick up a settlement or two on the way.
If you want to risk building inland, then you need to do the homework: figure out how many settlements are left to be placed and if you were the other people, where would you put them. Take your time in the initial setup, there are no time limits. If you don't want to go through this trouble (and other people saying "come on and place already"), build out. This may not be possible if you are placing first.
Remember, Wood-Brick people will build faster. Take into account your road-building capability, and of others near you. If you are Wood-Brick and an in a good position to build inwards (you have supply of wood and brick, and your turn placement is optimal), utilize your strength.
8) Connecting Settlements
If you are going for the longest road, you will need to connect your initial settlements eventually. If you are not going for the longest road, don't worry about it. It is usually more advantageous to wait to connect your settlements, if you possibly can. In either case, it is optimal to point your first roads at two different future settlement locations, so you can beat other people there. Note if you play it safe and point both towards your third settlement location, thinking you only need one more road to connect them, you will be one road behind for your fourth settlement. If you connect your two settlements, you will be two roads behind for your fourth settlement.
It is much harder to get blocked in when your settlements are in two vastly different locations. This is especially important for Ore-Grain people, who may have to wait a bit until they can build roads.