This is the eighth part in a series on historical linguistics, using Terry Crowley and Claire Bowern's Introduction to Historical Linguistics as a base. Part I is here. Part II, here. Part III, here. Part IV, here. Part V, here. Part VI, here. Part VII, here.
Having covered all of the features of assimilation, dissimilation should be a piece of cake. It's just the inverse of assimilation: instead of sounds becoming more similar due to proximity, they become less similar.
A classic example of this is Grassmann's Law. It's a highly specific law, in that it only works in Greek and Sanskrit, but the name comes from the nineteenth century when the discovery of law-like sound changes was considered entirely reasonable. The law may be simply stated: if an aspirated consonant is followed by another aspirated consonant in the next syllable, the first aspirated consonant will lose its aspiration. This is dissimilation because the sounds become more distinct from one another in terms of their phonetic features. Technically, it's dissimilation at a distance - the counterpart to assimilation at a distance - because the two sounds are not adjacent.
Crowley's example is the word 'bid'. In both Greek and Sanskrit, it derives from the same proto-Indo-European root (as does the English word). Grassmann's Law operated on this word in both languages in the same way.
*phewtho > pewtho
*bho:dha > bo:dha
Grassmann's Law developed independently in each branch, as far as I know, which makes it quite an interesting phenomenon. Not really a law, though.
Crowley's other example is from Afrikaans. Afrikaans is a dialect of Dutch, and they are mutually intelligible languages, although I believe it is easier for Afrikaans speakers to understand Dutch speakers than vice versa. There have been some significant sound changes in Afrikaans, including this one:
*sxo:n > sko:n 'clean'
*sxoudər > skoudər 'shoulder'
This is a regular sound change in Afrikaans. The voiceless velar fricative [x] becomes a voiceless velar stop [k] after [s], a voiceless alveolar sibilant (a kind of fricative). [x] and [s] are both fricatives; [k] is a stop at the same place of articulation as [x], dissimilating the fricative element of the [s].
And that's dissimilation. It relies on the same principles as assimilation, but backwards, making the sounds distinct.
Next time, tones and tone changes.