A valley is, technically, anything on the map that isn't a city. Each valley corresponds with a certain resource, except for flats, but we'll cover that later. The list is as follows:
Swamp: Food (but less than lakes)
Grassland: Food (but less than swamps)
When you take over a valley, you get a certain bonus to production of the corresponding resource. Mousing over the valley in map view will tell you the specific bonus. Don't bother with swamps and grasslands, they're not as effective as lakes. You can own as many valleys as your level of Town Hall -- if you have a level 3 TH, you can have 3 valleys.
Flats are used solely to build a new city. There is absolutely no point to owning a flat unless you intend to build a city on it. They take up room in your town hall, meaning you can't have a valley that's doing something for you, and they don't do anything for you. Don't bother with flats unless you're making a city.
How do I take over a valley?
First of all, when you click on a valley, does it have someone's name after "Lord" or does it just say "Lord: -- " ? If it has someone's name, then it means it already belongs to someone else. Do NOT attack the valley if it belongs to someone else unless you know what you're doing! Check the other player's prestige, alliance, etc. -- don't attack if they're in an alliance in the top 20, or have a sister alliance in the top 20, and don't attack if the player has high prestige. To be safe, don't attack at all if it belongs to another player. You could start a war!
Okay, so you've established the valley is unoccupied. You take over a valley by sending troops to it to fight the resident troops. Your troops have to win. At this stage, only take valleys that are not owned by another lord, because taking other players' valleys can start wars. To check this, just pay attention when you click on the valley -- if it belongs to someone else, it will read a Lord's name and prestige where it would otherwise be blank if it were unowned. Always scout a valley before attacking it, but to give you a general reference about the troops required to take valleys:
Level 1: 50 archers
Level 2: 100 archers
Level 3: 200 archers
Level 4: 400 archers
Level 5: 750 archers
Level 6: 1,500 archers
Beyond level 6, it varies too much to give ballpark numbers. Just think: LOTS.
When you successfully take over a valley, your troops will remain camping there. When they are camped at a valley, they will consume food at a highly accelerated rate, often pushing your food production into the red negative numbers. Just recall them by going to the valley on the map, clicking enter, and then hitting recall.
My Town Hall is full... what now?
You can continue to successfully attack valleys after you've gotten as many as you can conquer. While your troops will not conquer any additional valleys you attack, they WILL bring back resources that correspond to the type of valley. (Attacking a forest will yield you lumber, etc.) You will also gain experience for your hero by attacking them. There's also a small chance that you will get medals awarded to you from attacking valleys, and medals are VERY useful. You don't need them right now, but I guarantee you that if you keep playing, the day will come when you would kill everyone in the game just to find ONE MORE rose medal.
In short? Keep attacking those valleys. For levels 1-4, using the above numbers of archers will guarantee you a win.
*** NOTE FROM Silvera: I uses 800 archers, 1 sword, 1 pike and 1 scout to attack valleys for medals in ageII. Works fine for me! ***