How is it decided which words in a dictionary have illustrations?
If different dictionaries decide differently, I'd be satisfied just
knowing how one of them does it.

Hi uniace!
The following references should give you an idea of how is it decided
which words in a dictionary have illustrations:
  
Collins COBUILD New Student's Dictionary
"The illustrations have been specially chosen to help clarify
different meanings of the same word, or differences in meaning between
similar words, or simply to show exactly what something looks like."
http://www.athel.com/cobuild/illus.html 
  
Oxford Advanced Learner's Dictionary 
"We never choose to illustrate words merely to decorate or 'enliven'
the page. It would take too long to spell out our policy in detail,
but the underlying principle is to give a picture only when it can
help a user's understanding of the word, either because he or she may
never have seen the thing being defined (as with certain
culture-specific items) or when a picture can do the job better than
words." - Jonathan Crowther, editor of the OALD, 5th edition
(2nd last paragraph)
http://www.teflfarm.com/teachers/reviews/winners/oald.htm
  
Canadian Picture Dictionary
"Captivating illustrations reinforce meaning and engage young
learners. Children may use this dictionary as a stimulus to make
connections between objects, actions, words and feelings. Family
members reappear in sentences and illustrations to reinforce familiar
settings for the reader." (Publisher's Description)
http://www.curriculum.org/occ/resources/k3neldictpic.shtml
   
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I hope this information is useful!
regards,
Jack