You are established on any navaid facility tracking (LOC, VOR, NDB etc.) when within the tracking tolerances for that facility, and your tracking is such that you will be able to maintain this.
On that basis for a LOC, you are established, when, as earlier posters have indicated, you are within 1/2 scale deflection (1 dot).
A common error I frequently observe, is that many pilots will call "established" when the Flight Director or Auto-Pilot annunciates 'capture', this will frequently occur when still at full scale deflection. ATC are NOT aware or interested in your F/D or A/P modes, only that you are stabilised within the required tracking tolerances.
Regards,
Old Smokey