For controlling "cellpadding" in CSS, you can simply use padding on table cells. E.g. for 10px of "cellpadding":
For "cellspacing", you can apply the border-spacing CSS property to your table. E.g. for 10px of "cellspacing":
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.
Note: For a great overview of CSS properties that one can apply to tables and for which browsers, see this fantastic Quirksmode page.