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First of all open up the style sheet(s) affecting your site (e.g. style.css in your theme folder). Look for declarations relating to table element properties and modify them appropriately (after making a backup of the original). They should include something like this:
table { border-collapse:collapse; }
td { margin:0; padding:0; border:1px solid black; }
Upload and test to see if the desired changes have taken place. If they're still not behaving correctly then you will have to scour your css file(s) and page source for class's and/or ID's that are controlling the style properties of yor tables. If you're noticing that table cells are having an alternating background colour applied to them try commenting out the .odd and .even classes from your style sheet.