The following is a transcription of the speech Hermione made to Harry and Ron, detailing the goals of the society.

Our short-term aims are to secure house-elves fair wages and working conditions. Our long-term aims include changing the law about non-wand use, and trying to get an elf into the Department for the Regulation and Control of Magical Creatures, because they're shockingly underrepresented.
Two Sickles buys a badge, while the proceeds fund our leaflet campaign.

As I mentioned above, this is only a transcription of Hermione's speech. Our goals may change over time, but this is what we are starting with.