Set cellpadding and cellspacing in CSS?

Basics
For controlling “cellpadding” in CSS, you can simply use padding on table cells. E.g. for 10px of “cellpadding”:
td {
padding: 10px;
}

For “cellspacing”, you can apply the border-spacing CSS property to your table. E.g. for 10px of “cellspacing”:
table {
border-spacing: 10px;
border-collapse: separate;
}

This property will even allow separate horizontal and vertical spacing, something you couldn’t do with old-school “cellspacing”.
Issues in IE ≤ 7
This will work in almost all popular browsers except for Internet Explorer up through Internet Explorer 7, where you’re almost out of luck. I say “almost” because these browsers still support the border-collapse property, which merges the borders of adjoining table cells. If you’re trying to eliminate cellspacing (that is, cellspacing=”0″) then border-collapse:collapse should have the same effect: no space between table cells. This support is buggy, though, as it does not override an existing cellspacing HTML attribute on the table element.
In short: for non-Internet Explorer 5-7 browsers, border-spacing handles you. For Internet Explorer, if your situation is just right (you want 0 cellspacing and your table doesn’t have it defined already), you can use border-collapse:collapse.
table {
border-spacing: 0;
border-collapse: collapse;
}

Note: For a great overview of CSS properties that one can apply to tables and for which browsers, see this fantastic Quirksmode page.

Default
The default behavior of the browser is equivalent to:
table {border-collapse: collapse;}
td {padding: 0px;}

         
Cellpadding
Sets the amount of space between the contents of the cell and the cell wall
table {border-collapse: collapse;}
td {padding: 6px;}

        
Cellspacing
Controls the space between table cells
table {border-spacing: 2px;}
td {padding: 0px;}

        
Both
table {border-spacing: 2px;}
td {padding: 6px;}

        
Both (special)
table {border-spacing: 8px 2px;}
td {padding: 6px;}

Note: If there is border-spacing set, it indicates border-collapse property of the table is separate.

Try it yourself!
Here you can find the old HTML way of achieving this.