I agree with all that mzabsky said in his answer.
Here's a few of extra things:
I find it useful to make statements using a Text
or DisplayFormula
cell then manually group a Mathematica check/proof to the statement which is then collapsed and can be displayed when you want.
The Writing Assistant Palette has quite a few useful constructions in it that you can learn from.
Finally, I found it really useful to make my own style sheet for a couple reasons:
1) the built-in ones are a bit ugly; 2) it really helps you to understand how the notebooks work.
To see examples of the stylesheet I made (which I don't claim to be perfect - I didn't bother making it work in all screen environments) look at some of the files in ftp://ftp.physics.uwa.edu.au/pub/MATH2200/2010/. I use a similar stylesheet in all of my notes - I have many research projects primarily contained in Mma notebooks, eg http://arxiv.org/abs/1102.3043.
Like Mr Wizard, I also recommend David Park's notes as a starting point. Also, you should study stylesheets that you like by going to the Format menu and clicking "Edit Stylesheet". Don't forget to follow the links through the cascade of stylesheets (version 6 onwards).
To answer the questions in your edit: Once you are viewing a notebook's stylesheet, you can save it, edit it, and use it in your own documents. Stylesheets in
$UserBaseDirectory/SystemFiles/FrontEnd/StyleSheets
are automatically available in the menu. You can then use that stylesheet in any notebook by simply selecting it from the menu.
The formating in the screenshot that you posted is all contained in the stylesheet. This includes the grey background in the table.
Addendum:
When distributing notebooks to others, if the stylesheet is external from the notebook, then other people will not see it as you do. To include the stylesheet into the current notebook, you need code like
ss = StyleDefinitions /. Options[EvaluationNotebook[]]
fn = ToFileName[{$UserBaseDirectory, "SystemFiles", "FrontEnd", "StyleSheets"}, ss]
If[FileExistsQ[fn],
style=Get[fn];SetOptions[EvaluationNotebook[],StyleDefinitions->style];,
Print["Can not find file"]]
(Assuming the file is in stored in the conventional place)
Here's an EmbedStylesheet.m that is an improved version of the above.