Since I tend to lose everything, I don't take my engagement ring off (except at night) so it tends to get really dirty. Rather than head to the jewelry store or buy expensive jewelry cleaner, I decided to try to clean it myself.
I placed my diamond ring in the bottom of a small ramekin and added enough distilled white vinegar to completely cover it. I let it soak for about 30 minutes and then gently cleaned it with a soft brush. Be very careful when using the brush since you definitely don't want to damage the prongs holding the diamond on your ring.
After the soak and brushing, all the gunk was off the diamond, and it looks like new again!
Please note: I used vinegar to clean my diamond and gold ring. You'll want to be very careful about cleaning a variety of gems in natural cleaners, especially pearls. Be sure to do some research for your type of gem.