An easy way to keep your jewelry looking beautiful is to soak it in a gentle degreasing solution such as water with a few drops of mild dish soap. After you remove the diamond from the cleaning solution, use a soft, clean toothbrush to remove any remaining dirt.
There's no specific time when your piece will need cleaning - it's really based on the piece and how you wear it. If you wear a piece everyday, it will need cleaning more regularly than a piece you only wear on occasion. Generally, if your piece has settings or lots of intricate detail with more spaces and little tight areas for dirt to build up in then it will need cleaning more frequently than something simpler in design. If you have a plain band with no stones then it will probably never need to be cleaned as there's nowhere for dirt to adhere to. The best thing is to go by eye and clean your pieces when you notice them losing their sparkle.