Here's the help file, which I think can get confusing because help edge actually takes you to one of the sphere lists for some reason:
Level(0) EDGE EDGES
Edges are specialization options open to all characters. They are generally
much lower in potence and importance than other class specialization choices,
such as a ranger's terrain, a warrior's specialization, and so on. Edges
grant a character advantages while using certain skills/spells/supplications
or under certain circumstances, but do not add new skills to a character's
repertoire.

A character may qualify to select a specific edge based on a number of
factors, including but not limited to their class, race, alignment, ethos,
proficiency level in a given ability, and permanent attributes such as
strength or intelligence.

Characters earn the right to choose additional edges through excelling in any
of several areas of play, including RP, PK, exploration, commerce, quest
participation, cabal activities, and so on. Quality characters of very
different types will earn the right to pick a good number of edges; a
character who excells in many areas of play (for example, a skilled
playerkiller also recognized for their exemplary roleplay) will have the most
opportunities to choose edges.

To see which edges you may currently choose, DISCUSS with your guildmaster.
To choose an edge for which you qualify, "discuss
guildmastername 'edgename'".

For edges that have the ' symbol contained in the name (e.g., Kindred's
Touch), enclose the full name of the edge in double quotes when you discuss it.

The EDGES command will display the edges you already have.

See HELP EDGE LIST to see additional helpfiles with lists of edges. These are
also constantly being added and may be a little slower than the initial
release of a set of class edges. Thank you for your patience.





So all that said - you accrue edge points exploring, using commerce, and observing. Imm xp plays a big role too, so writing a role is very helpful. Your guild master will tell you all the edges you are currently eligible to take with the points you have, but once you use the points, that will change.