We’re focusing on English nicknames in this post, but you can see a selection of diminutive forms in other languages in the entry for the name. For as popular the name was, it was surprisingly nickname free, in comparison with other names of similar popularity where we have many different and disparate diminutive and hypocoristic forms attested.
So, you start off Richard and lop off the end, to create the hypocoristic form Rich. The Middle English pronunciations of the root name encompassed a pronunciation with a hard \k\, which is how you get Rick as well as Rich. Since Dick is the one we’re interested in, we’ll set aside Rich and all the diminutive forms we can get from that.
The step from Rick to Dick and Hick comes easily, as they are rhyming forms. In fact, Withycombe, s.n. Richard, notes that these were “among the earliest of this kind of rhyming nickname, the first example noted being a record in 1220 ‘quidam Dicke Smith. Dick itself was sometimes augmented with a diminutive suffix, such as -el, -et, or -on, as found in, e.g., Dicun 1206, Dycket 1296, 1219 (and it’s diminutive Dikelin 1275), all from Reaney & Wilson s.nn. Dicken, Dicketts, Diggle. Similar diminutives of Rick can also be found, with Rikelot 1191-2, Ricot 1327, and Ricun 1274 (R&W s.nn. Richard, Richings).
We will end with a curiosity: A nickname that we know is a form of Richard but which we don’t really know how it came to be such, is Hud(de). Both Withycombe and Reaney & Wilson (s.n. Hudd) reference Bardsley’s examples of one Ricardus dictus Hudde de Walkden 1346 and another Ricardus de Knapton et Cristiana hud-wyf 1379. Hudd is usually more often a nickname of Hugh.