Edge points can be accumulated through gaining exploration and observation points. There's a chance commerce might also count, and is definetly a factor in gaining some edges (see Shrewd Trader, I've had this offered at various levels of the haggle skill so it's certainly commerce related). This is how I gain most of my edge points.
There appear to be 'shelves' you reach in your pk history where you are awarded edge points. How this is judged is unclear, killing more powerful foes might help or it could just be numbers, but being a 'good pker' does net you hardcoded edge points.
It's unclear how ranking and age play into but I will say this - You gain a nice edge bonus for reaching level 51 :) Yay heroing! It's usually enough to buy you a mediocre edge and with some arrpee guarantees a nice edge.
If you read the edge helpfiles, the skills mention at the bottom are usually pre-requisits. Getting these skills into the 85-95 skill range and then accumulating enough points is usually enough. Some skills rely on your gank-o-meter (Ehren soul, Ehren Lord, see Premium Battlefield Forum - PBF - for details on that) others rely on just having a large amount of kills (Murderous reputation, Sounder of the Knells).
For further help on any specific edge, see the DIKU-Wiki on the left. There's a page dedicated to edges.
Anyone got anything to add/correct?
Yhorian