There you go, the best spot on the board. Blue, or player #1, wisely placed his first settlement on this spot. Hopefully this was also the spot you identified. Now, let's go over the reasons this is the best site for a settlement in Catan.
1) Count Dots - The first thing you should do to evaluate a potential site for a settlement is count the number of dots on the numbers it is next to. To understand what I mean by this, take a look at the circular tiles with numbers on them which mark the number to be rolled for a resource tile to produde. You should see under the number on each of these tiles a number of dots. Each dot represents a combination of dice which could be rolled that will result in that number being rolled. All you need to understand, though, is the more dots under a number, the more often that number will be rolled, and therefore the more resources you can expect to get from a tile with that number on it. The best numbers (six and eight) have five dots, while the worst (two and twelve) have one dot. So, to get an idea for how many resources a specific settlement location will give you, total up the number of dots on numbers on the three adjacent resource tiles. The highest total you can expect to see is 13. A settlement spot with a total number of dots 11 or higher will give you a lot of resources. As you can see, the spot the blue player picked had 12 dots. This is tied for the most number of dots a settlement location on the board has.
2) Resource Types - Next to the number of dots a potential site for a settlement has, you should look at what resources that site can produce. If you have not yet picked one of the three overall strategies for victory in the game, a site with wood and brick or with rock and wheat is the most valuable, since it sets you well on your way to winning with one of those two strategies. If neither of those is available, then try to find a site with some other set of resources which work together. Just make sure to avoid something like a site with wood, ore, and sheep, unless you are set on using the middle road path to victory. If you aren't sure what I'm talking about with these different overall strategies to victory, then read my basic strategy page. As you can see, the blue player picked a great spot by choosing one with a lot of brick and a lot of wood. He could have picked the 9 (wood), 6 (wheat), 10 (sheep) spot nearby, since that one also has 12 dots. However, the resources on that one don't work as well together since there is no brick-wood or wheat-ore combo.
3) Nearby Ports - The last thing to consider when placing your first settlement is what ports are near your settlement. I list this piece of advice third because it is pertinent to the placement just made, though when you are placing settlements later in this initial phase you should value expansion opportunities (which I will discuss later) more than ports. You should never place a settlement on a port start to begin, but it is always nice to be near a 2:1 port of a resource you will be generating a lot of. In my opinion, this part of your strategy should considered if the above two pieces of advice don't make it abundantly clear which spot to put your settlement on. In any case, though, you can see that this starting spot for the blue player is even better than normal due to the nearby brick port. Since he/she already has a settlement on an eight brick, the blue player can be sure that 2:1 port will get a lot of use.
Now that the first player has picked the best spot on the board, the second player now must do the same with the remaining open spots. The second player should follow the same advice as the first player since there are usually two great spots to start the game off. Look at the map again and identify which spot you would put your first settlement on if you were the second player, then keep reading to see if you picked correctly.