Two part question:  How did "Dick" become a nickname for "Richard"? 
How did "Bob" become a nickname for "Robert"?  The answer needs to be
better than a variation of "Sound's like Rob".

The best answer I have found is from a recent staff report on The
Straight Dope:

"What came first, Dick or 'dick'?", by SDSTAFF Dex (22-Aug-2002)
The Straght Dope
http://www.straightdope.com/mailbag/mdick.html

According to the report, back in the days of Old and Middle English,
everything was written by hand; "it was therefore common and easier to
use agreed-upon abbreviations."  An example of an abbreviation was
"Ric." for "Richard".

The abbreviations led to diminutives, such as "Rick".

Rhyming nicknames were fairly common in the 12th and 13th centuries,
such as "Hick" and "Dick" from "Rick".  "Dick and Hick were among the
earliest of the rhyming nicknames, first appearing in writing around
1220.  Other rhyming nicknames include Polly from Molly, Bob from Rob
(from Robert), Bill from Will (from William); and Hodge from Roger."

Dick has remained a nickname for Richard.  "'Hick' has thankfully
become obsolete, except when tied to 'Dick' in rhymes such as
'Hickory, Dickory, Dock.'"

A web site on the etymology and history of first names in English
agrees that "Bob" is a medieval "rhyming nickname" for Robert.  This
site also suggests that the change in the initial consonant from
"Rick" to "Dick" may have been caused by "the way the trilled Norman R
was pronounced by the English."

"Bambi-Cassidy"
Behind the Name
http://www.behindthename.com/nmc/eng2.html

"Darrell-Elvis"
Behind the Name
http://www.behindthename.com/nmc/eng4.html
 
- justaskscott-ga


Search terms used in Google (used in various combinations):

diminutives
nicknames
"rhyming nicknames"
rick richard
bob robert

Stellar research!