Evasion starts at every battle for every Pokemon at 0% and rises depending on the move or abilities as they come into play.
As for increments, it doesn't seem to be all that well documented. Sand Veil will raise your Pokemon's evasion by 20% according to Bulbapedia, but most other talk of it refers to it as incrementing levels.
Minimize prevents you increasing evasion at all after +6 levels, so this could be 60% - so it can probably be assumed that every, or most, attacks that affect evasion do so in increments of 10%. There's really no other way to make sure of this information without hacking it yourself from the games though...