1. How Can I get more of an income of gold.
This is where micromanagement comes in.
Every single tile has its own values. For example, grassland is 2 food, desert is 1 shield, etc. Food is how fast it grows, shield is how fast it builds, and commerce is how much money that city makes for your treasury.
What you want to do is to tweak every single city the way you want it...most likely checking on each one every single turn. If you are building a Great Wonder, try moving around all your guys so that they are working on the tiles that give the most shield. If you are running a deficet, do the same for commerce.
Also, beware of
corruption. The further away from your nearest Palace, Capital or Forbidden Palace (in general, but not to be technical), the more commerce you loose, and the less money you gain per city. Also, on Despotism, if you get more than 2 food, then it is subtracted one. For example, if you are on grassland and you irrigate it so that it produces 3 food, then if you are on Despotism, 3-1=2, so you still only gain 2 food because of production.
Sometimes, if there are more unhappy citizens than happy citizens (content citizens don't matter), then you will most likely need an entertainer or an increase in the luxury slider to keep them from going into disorder (no production, commerce, or growth). To do this, just click on one of your laborer's worked tiles and they will disappear and turn into an entertainer (or a scientist or a tax collector - you choose). However, this gives you less laborers to work the tiles.
If you don't want to micromanage that way, then use the Governor. Right-click on a city, and then select "Contact Governor". Then set your options - do you want your laborers to automatically go for the shields, foods, or commerce?
Also, if you press F1 or F2 (forgot) or F3, there will be two little sliders at the top. One is the science research. The higher this is, the faster you research. The other is the luxury slider. The higher it is, the more money is devoted to keeping your citizens happy (you don't need to touch this in chieftan - disorder doesn't come very often if you micromanage correctly).
2. How Can I get cities that aren't growing to grow.
Either contact the governor or micromanage yourself, moving around all the laborers so that they work on the tiles that will provide the most food. Also, cities cannot exceed Size 6 unless they are next to a river or have an aqueduct built in them. Cities cannot exceed size 12 unless they have a hospital (available in Industrial Ages).
If your tiles just aren't giving enough food no matter how you twist them, then irrigate the tiles. Unless you have Electricity, you cannot irrigate unless there is fresh water (a river or a lake) nearby. So, if you want to irrigate in the middle of the desert, you have to make a long irrigation chain from the nearest freshwater source.
Tundra cannot be irrigated. Only mined. Mines produce more production (shield) when worked, and can be built on any land terrain except for Flood Plains.
3. How could I beable to get a very large army like I see in some of these screenshots on this site.
To get an "Army", you have to win a battle with an Elite (using a Land Unit). There is a 1/16 chance of you getting a Military Great Leader. Then, move him to the nearest city and create an army there.
If you are talking about lots of forces, just build, build, build!
Also, tips for a newbie - expand expand expand. New cities are your most valuable assets up to mid-Ancient Era.
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j/k! I think you meant to ask how to make cities grow?
