Evangelical Outpost links to a page describing the Dominic System. I confess, looking it over, I prefer the Major System, which I once taught to myself. (Now that it comes up, it occurs to me that I almost never use it. And I should; I have a horrible memory for numbers, and that's where the Major System works best.) Under the Major System, you would convert a numerical string into a string of sounds. For instance:
Then you use vowels to expand this sound-string into something capable of being mnemonic, e.g., BRANDON. You can then reconvert whenever you need to do so. The bulk of the actual memory work, under this as under every other system, is in a further conversion to images: I associate an image with the word BRANDON, recall the image, convert to the label, and convert to the numbers. Although, I confess, since I have a very verbal mind I often just use the mnemonic words, supplementing with images as needed.
Under the Dominic System, the above number would be converted into:
which the Dominic System can't even handle on its own, since it doesn't have an even number of elements. Now, I have no doubt that the Dominic System, fully worked out, is probably much better than the Major System for speed memorization, but I ask you, how often outside a speed memorization contest will you really need to memorize long strings of numbers all at once? The Major System is a much more flexible system than the Dominic System, since it can be tailored to any number-memorizing need you might have. Here is an article on using the Major System.