First, it is important to understand what we mean by a satire. Satire is often likened to irony because it is meant to show abuses or shortcomings.
In the educational system, we see the rules are ignored. Students should be in school but this is not really enforced. Many show up for a day or two and disappear.
In the judicial system, equality and fairness is seen as a farce because a many is wrongfully convicted just because he is a black man. This ties in with the idea of democracy because evben though Tom was entitled to a fair trial, he really did not get one and this system did not work for him.
In religion, where we are not supposed to judge and all should be accepted, we see Jem and Scout unaccepted in a black church because they are white until they people realize their dad is helping Tom.
There are many examples of each of these institutions being satirized, but I will give you a few. First of all, education is satirized because Scout is chastised by her teacher for reading too well! The court system and democracy are satirized in that they both fail miserably. Tom Robinson is unjustly accused and tried for a crime he did not commit because of his skin color, and there is no democracy for him nor hope for freedom. Religion is satirized when Calpurnia takes the children to her Black church and the congregation is prejudiced against Jem and Scout because they are White. Also, in a town that thinks of themselves as religious, there is little evidence of any religious precepts. Look further at enotes links for more ideas!