Try not to get bogged down too much in the political and literary allusions, but concentrate on the comedy and broader themes. But Aristophanes is a very political writer, so as you read these plays, try to figure out what (if any) political orientation he has.
Outside of the obvious, think about the main differences between Athenian comedic and tragic dramas (staging, character types, plot form, role of chorus, etc.)
For those of you who associate comedy with Cheers, the aggressive, liberating scatological (look it up) comedy of the Greeks will come as a bit of a shock. We're from moving characters who commit suicide out of shame to characters who don't know what the word means. What can you say about a culture that contains both attitudes? Note the heightened awareness of what is now called "the fourth wall"; the characters occasionally address the audience. Note also the heightened awareness of language and of being on stage (i.e. lots of "take my wife, please" jokes).
The Frogs is considered to be the last play written under the aegis of "Old Comedy," and was composed during the last year of the War (404). This is no accident, as Old Comedy depended on freedom of speech. A city that in 399 would kill Socrates out of annoyance would have been in no mood to have its leaders' sexual habits openly ridiculed. Aristophanes could say things no modern comic would even dare
This is the second play we have read where Dionysus is the lead character. Is Aristophanes thus trying to say something about the theater? Compare the two Dionysuses (their portrayals and purposes have more in common than you think at first) and the plays' plots. Note that he goes down to get Euripides but returns with Aeschylus: why does he change his mind?
Look for parallels between the slapstick first half and the more intellectual second half.
Why does Dionysus borrow Heracles' clothing for his journey? What comic circumstances does this disguise create?
The journey to Hades is a traditional act of mortal heroism. Is there any significance in having the god undergo this trial? How does he acquit himself in the horrors of Hades?
Look for any indication of why Sophocles is not considered a candidate for resurrection. Do you find any truth in the criticisms leveled against Aeschylus and Euripides? Which, if either, does Aristophanes treat more harshly? Is he unfair to them? Consider the moral and aesthetic criteria by which he judges the dramatists. What is the function of a playwright, according to this play? Consider this in the light of Aristophanes' own plays. Plato later, especially in theRepublic, develops many of Aristophanes' insights. The Frogs is considered (by some) to be the first work of literary criticism.