To keep jewellery looking like new is impossible if you plan on wearing it. You have to realise that the dulling of the jewellery is divided into different reasons and each reason has a different remedy
a)The metal scratches- You can use a polishing cloth with a small amount of success. The only real remedy is to have the ring professionally polished at a jeweller. Bear in mind that each time you polish a jewellery item a tiny layer of metal is removed. I would say that in normal conditions it isn’t necessary to polish an item more often than once a year.
b)The stone becomes duller with wear- This is the result of natural oils and hand-creams coating the back of the stone. All stones are influenced, especially paler coloured stones. Diamonds are least affected. Use an old tooth brush and diluted dishwashing liquid with luke-warm water. Make sure the plug is in the sink!
c)The metal discolours- This depends on the metal. If it is a white gold item then refer to the previous point regarding rhodium plating. If it is 9ct gold you have to realise that pure gold is chemically inert, but there is only 37.5% pure gold in 9ct. The atmosphere and specifically mineral rich liquids or household chemicals can react with the other metals in the alloy resulting in tarnishing. Silver naturally oxidises to form a black or brown layer on the surface of the silver. With both the 9ct and the silver problem you can either use a jewellery polishing cloth if the tarnishing is on the surface or you can use a jewellery cleaning liquid if the tarnish is in recessed areas. Make sure you read the directions on the liquid, most only require a few seconds of liquid and then rinsing with water. Using a brush with the cleaning liquid often helps.