When you have built up enough of the required experience and met certain prerequisites for edges, they will appear in a list when you discuss with your guildmaster. If you don't see any edges, then you are either not a high enough level, didn't get enough of the right kinds of experience, or else didn't get your stats/skills to a high enough level to learn any.

If you want edges, most people start seeing them at about 20th-25th level, although probably nothing too exciting until later. Try having a good description and a page or two of a well-defined role, so you might gain a small bit of Imm experience early on. Also, try looking at everything you can, particularly items in rooms that you wouldn't normally look at (like that dresser, open tome, or journal entries you find lying around) for some observation experience. And if you can find hidden rooms, really explore them well, as every little bit of observation experience helps in the long run.

As far as improving at an edge, they aren't really like skills. They either make certain skills a little better, or change them slightly. They will always be "on" as long as you are doing whatever it is that makes those skills/abilities work.

Most edge lists are in the helpfiles and will show up if you search for EDGE LIST. If there is some kind of a prerequisite, it is usually strongly hinted at in the helpfile.