It's show and tell time. I'll show you pictures of tabs and indents, and I'll tell you how to create the effect. Or, at least I'll point you to the Help topic that tells you how to do it.
Simple tabs
When you press the Tab key, the insertion point moves to the next tab setting. If you haven't manually entered any tab settings, default tab settings appear every 3p. These tab settings don't appear on the Tabs ruler.

1. Choose Type > Tabs to display the Tabs ruler (also called the Tabs dialog box).
2. Click above the ruler where you want the tab setting to appear.
3. On the left side of the Tabs ruler, click to indicate which type of setting you want (Left, Center, Right, or Decimal).

See the Tabs and indents Help topic.
Decimal tabs
You probably noticed that in our example, the tabs are left aligned. It looks better if it's decimal-aligned or right-aligned, like this:

You can get away with right-aligning currency figures because there are always two decimal places, but you really need the decimal align option when decimal numbers vary, like this:

By the way, you can use any alignment character. Just delete the period (.) in the Align To box on the Tabs ruler and type a different character. See Specify characters for decimal tabs.
Tab with dot leaders
To add dot leaders to the tab, type characters in the Leader box. Here I typed a period:

I think the periods are too close together, so I added two spaces before the dot leader:

Ah, much better! See the artless Add tab leaders Help topic.
Indent to here
If you've spent a lot of time in Microsoft Word or WordPerfect, you may wonder how to insert an indent. In InDesign, the trick is the Indent to Here character. Place the insertion point where you want the rest of the paragraph to be indented and choose Type > Insert Special Character > Other > Indent To Here. It works especially well in drop caps:

See the Use Indent to Here Help topic.
Right-aligned tab followed by left indent
Here's a tab effect that's undocumented in Help. When you're laying out a screenplay, how do you right-align the first tab setting and then right-indent the second one?

Add a right-align and a left-align tab settings as shown. That's easy enough. Then, insert the Indent to Here character in each paragraph so that the left tab essentially becomes a left indent. Oh, and make sure you press Tab to insert tabs in all the right places. It's easy to forget that tab settings affect only tab characters.
When I write the Great American Screenplay, I'll use tables with invisible borders to achieve this same effect. But you may need to use tabs for whatever reason.
Simple indent
Let's turn our attention to indents. I created this indent by dragging the markers in the Tabs ruler.

First line indent
Instead of pressing Tab at the beginning of every paragraph, create a first-line indent.

See Set indents using the Tabs dialog box Help topic.
When working with tabs and indents, you can either drag the markers in the Tabs ruler, or you can enter numbers in the Control panel or when creating a paragraph style. It makes more sense to create first-line indents as part of a style:

See the Add paragraph and character styles Help topic.
Hanging indent
A hanging indent is also called an "outdent." Hanging indents are usually used with bulleted or numbered lists and run-in headings.

See the Create a hanging indent Help topic.
Hanging indents with bullets or numbering
Whenever you need to indent the text in bulleted lists and numbered lists, just remember to include offsetting values in the Left Indent and First Line Indent fields.

To indent text in outlines, see this article I wrote a few months ago on creating outlines.
Right indent last line of paragraph
In sales brochures, it's common for the price to appear at the end of a paragraph. If you want the price to be right-aligned, place the insertion point before the price number and choose Type > Insert Special Character > Other > Right Indent Tab.

See the Right-indent the last line of a paragraph Help topic.
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Did I miss anything? Got ideas for other galleries? Leave a comment. I finally figured out how to maneuver through my new spam filter -- all comments are now flagged as spam by default -- but I'll go through my comments list every day.

Hi,
Very helpful article, thanks! To push my luck, do you know if there is any way of setting up a paragraph style to do this bit?:
"You can get away with right-aligning currency figures because there are always two decimal places, but you really need the decimal align option when decimal numbers vary, like this"
(I use it a lot in tables and would be easier not to have to set the tabs for each column...)
__7.00
900.00
__9.00
__0.6782
etc..
Thanks for any help!
Tim