How do I create a basic table?

Tables are created via use of the double pipe character: ||. Lines beginning with this markup denote rows in a table; within such lines the double-pipe is used to delimit cells. In the examples below a border is added for illustration (the default is no border).

|| border=1 rules=rows frame=hsides
|| cell 1 || cell 2 || cell 3 ||
|| cell 1 || cell 2 || cell 3 ||

How do I create cell headers?

Header cells can be created by placing ! as the first character of a cell. Note that these are table headers, not headings, so it doesn't extend to !!, !!!, etc.

|| border=1 rules=cols frame=vsides
||! cell 1 ||! cell 2 ||! cell 3 ||
|| cell 1  ||  cell 2 ||  cell 3 ||

How do I obtain a table with thin lines and more distance to the content?

"Thin lines" is tricky and browser dependent, but the following works for Firefox and IE (Nov. 2009):

||border="1" bordercolordark="black" bordercolorlight="black" style="border-collapse:collapse" cellpadding="5" width=66%
||!Header || !Header|| '''Header'''||
||cells   || with   ||      padding||
||        ||        ||             ||

How do I create an advanced table?

See table directives

My tables are by default centered. When I try to use '||align=left' they don't align left as expected.

Use ||style="margin-left:0px;" instead.

How can I specify the width of columns?

You can define the widths via custom styles, see Cookbook:FormattingTables and $TableCellAttrFmt. Add in config.php : $TableCellAttrFmt = 'class=col\$TableCellCount';

table.column td.col1 { width: 120px; }
table.column td.col3 { width: 40px; }

How can I display a double pipe "||" in cell text using basic table markup?

Escape it with [=||=] to display || unchanged.

How to I apply styles to the elements of the table, like an ID to the table row, or a class/style to the TD?

See $WikiStyleApply.