To create a correspondence table, first look up each word in the source-language half of a translation example in a bilingual dictionary, and mark each occurrence of any of the translations in the target-language half as a possible correspondence. This yields a matrix such as the one in Figure 1. Note that there can be considerable ambiguity, especially for more common words such as determiners and prepositions.
Before actually using the correspondence table, we first prune it, removing those correspondences that are unlikely to actually be correct. To perform the pruning, we take advantage of the fact that there is usually local coherence between the two languages -- even if the word order is not exactly the same, a particular unit such as a noun phrase in the one language will usually correspond to a single unit in the other language, rather than being scattered all throughout the translation. Thus, for each word, we compute an expected range for its translation, and remove those correspondences which lie outside that range (ensuring that we never remove the last correspondence for any word in either language). The expected range for a word's translation is simply the range between the earliest and latest possible translation of its neighbors, expanded by a given number of words to allow for minor variations in word order. Should one of the neighboring words have no known correspondences, the expected range is set to be the entire sentence.
In Figure 1, we would prune the table by first proceeding downward, trimming each row as we go, and then proceed left-to-right, trimming each column as we go; this process repeats until no more correspondences can be removed. Consider the two green rectangles. These indicate the expected ranges for the words pointed at by the arrows on the left. For the upper rectangle, we can remove the two possibilities to its right, since neither is the only correspondence in its column, and we will still keep the third possibility in that row. For the lower green rectangle, nothing can be removed -- yet. When we switch to moving across the table, we eventually reach the red rectangle. Notice how we can now remove the two possibilities above the rectangle, which were unaffected during the scan down the table.
This example also demonstrates how the method is able to deal with large-scale rearrangement of the units in the sentence. Within each such unit, we have the same situation we would have had without the rearrangement. Only at the boundaries is there a change, which has the effect of making it harder for possible correspondences to be removed, since the expected range becomes larger. Harder, but not impossible -- as shown by the removal of the two correspondences above the red rectangle.