Okay, George, I’ll give it a shot.
First: producing a worker or settler costs your city population. If you produce a worker, your city will drop one population point. If you produce a settler, it will drop two points. This is done to simulate the idea that a part of your city’s population has up and moved out, to found a new city somewhere else.
This means that your first city must have a population of 2 before it can produce a worker. After producing that worker the city will temporarily shrink to 1, and then gradually go up again.
A city must have a population of 3 to produce a settler. It will immediately drop to 1 after the settler has been produced, and then gradually grow again.
Workers are necessary for tile improvement. At the beginning of the game they can perform four functions: build roads, build mines, irrigate, and chop trees.
If you build a road on a tile that is being worked by your city, it will usually generate +1 commerce. If you irrigate, it will produce +1 food. If you build a mine, it will produce +1 shield. So, to answer your second question, to increase shield production you should use your workers to build mines.
All of the above is modified, however, by the type of terrain you’re improving. So here is a general rule of thumb: mine grasslands (green) and hills. Irrigate plains (brown). Start by looking at your city screen and noting which tiles are being worked by population. Irrigate and/or mine those tiles first. A tile must be in use for its improvements to add to its production.
Roads are very important, because they add commerce, and commerce is the foundation of your society’s research speed.
Also, learn your terrain types. At this stage you need to at least have a vague idea their differences.
Chopping down trees generates a one-time 10-shield bonus to your city – provided the trees you’ve chopped down are within the city radius. Otherwise you’re simply wasting your chopping. Be aware as well that you can hack down jungle, but don’t get any bonus for that.
Regarding you science production: there are a number of so-called “advisor” screens at your disposal. One of the most important is the city advisor (F1). Use the city advisor to “macromanage” your civilization.
If you hit F1 you will find a luxury and science slider in the top right-hand corner of your screen. These sliders determines how you spend the commerce produced by your civilization. They can be set from 0 to 100%, but combined can never total more than 100%. The more commerce you produce, the higher you can set your science slider. This translates excess commerce into science beakers and hastens your technological advancement. The luxury slider affects citizen happiness: the more commerce you invest in luxuries, the happier your subjects become. But be careful to maintain a balanced budget! Always make sure your civ’s finances are “growing,” not “shrinking.” Excess money is saved, and can be used to purchase technologies from rival civilizations, or, at later stages in the game, to purchase city improvements.
Hope that helps.