Arguing by analogy can be done in one bold, sweeping statement. For example: "Just as it was wrong to deny women the vote, it is also wrong to deny the vote to children." It can also be a lengthy, involved process, in which two speakers agree that a rule or predicate applies to one state of affairs, then argue over whether another state of affairs is enough like the first state of affairs for the same rule or predicate to apply to it.
This is a waste of time, because analogies don't prove anything. An analogy can be useful to illustrate a point or explain something to someone who is unfamiliar with a concept. For example: "You are familiar with broccoli, right? Well cauliflower is like broccoli except that it is white" Analogies can also make an argument accessible or understandable to someone who is otherwise unwilling to be open-minded about it. For example: "Those who are unwilling to accept the possibility that animals deserve moral consideration should consider that much the same thing used to be said about racial minorities."
This example, however, is not an argument. It is an attempt to get people who are simply closed-minded to look at the argument (the one the analogy is trying to support) more neutrally. Logically speaking, trying to argue about one thing by talking about something else is pointless. If you think that the line of argument that led you to believe something about X might also apply to Y, don't talk about X. Apply the reasoning to Y and see if it works.
