IME you can get them as late as August, but it is well and truly dying down by then. For me peak season has always been May-June, but I haven't picked for a long time. Every couple of years I like to pop out and see if my old spots are still going, but I haven't been out this year.
Some mates of mine usually pick a large amount every year, but for whatever reason they didn't bother this year, so I can't comment on the picking climate this season at all.
Shroomery is a good resource if you want to learn how to pick. I taught myself how to pick by reading those boards in 2007 and had a great deal of success my first year, although it did take me a while to get my first find (funnily enough it was actually inside the grounds of my High School). Once you find them and truly know what you are looking for it is smooth sailing from there.