I would highly recommend starting to look for letter writers towards the end of your sophomore year. Cultivate the necessary relationships with your profs by going to office hours and making sure they know you by name. Also, once you've targeted the profs who you will be asking, keep in touch with them if you won't be applying for a few more semesters. This will make life a lot easier when you go to formally ask them.
I know too many other premeds who didn't even consider LORs and waited until after the spring semester of their junior year to ask profs for letters. Many had taken the course three or four semesters ago and the prof had no idea who the student even was.
I asked most of my letter writers in Feb or March and told them that I needed the letters by the end of May. This worked well because even though two of them took longer then requested, it still wasn't too late.
Oh, and have a few letters as spares in case someone doesn't come through. Scrambling in September for a rogue letter writer is hell.