Bofatron is right. Learning and improvement seem to take place in spurts, if you will. You might go for a long time just playing the same stuff, with your playing skills being on a plateau, and then all of a sudden, when you're starting to get sick of it, you'll get a lot better in the space of a week or two.

But anyway, I think after three months I was learning barre chords, playing some simple songs, and doing some improvisation with pentatonics. Of course, this will vary depending on how much you practice, what kind of a teacher you have, and how dedicated you are.