How did Shaver (1970) manipulate similarity in the defensive attribution study? Shaver (1970) had two independent variables, severity of the accident outcome (severity) and similarity of the subjects to the transgressor.

Severity was manipulated by giving subjects in different conditions different scenarios: 


mild outcome = the boy had the metal splinter in his wrist
severe outcome = the boy had a metal splinter in his eye


How did Shaver “manipulate” the IV similarity (similar/dissimilar)?

References

Shaver, K.G. (1970). Defensive attribution: Effects of severity and relevance on the responsibility assigned for an accident In: Journal of Personality and Social Psychology, 14(2): pp 101-113.
DOI: 10.1037/h0028777
This article has several experiments included in it. These have different operational definitions of variables, and specifically differ in their definitions of "similarity". I'll assume you are talking about Experiment 3 where the hypothetical child is injured. From the end of Experiment 2 (p. 108, c. 2, first full paragraph):


  ... a third experiment was conducted in which perceived personal similarity was one of the dependent variables ... Thus, only severity of consequences was
  actually manipulated.


So for this situation (Experiment 3), similarity is actually treated as an outcome and is not manipulated.