Talk to people. You can normally find side missions when there are people grouped together you've never seen before. Like 2 Yakuza looking types sort of overshadowing a shop owner. That's a cue that you can step in and do a side mission to beat the crap out of the Yakuza or do something a little more in depth.
There should also be a menu that will show you all the side missions that you've accepted and which ones you've completed. Apparently you can do almost every single one but about 5 or 6 are missable.
A post containing them can be found here.
Substories Achievement