@novishone: If F is hard to play on all 6 strings, you can use the 2,3 or 4 string version to begin with. That would be as follows:
1st fret on high/thin E string with Index finger
1st fret on B string with Index finger
2nd fret on G string with Middle finger
3rd fret on D string with Ring finger
First get the Index finger barring (= putting a finger at a fret on more than one string) right. If you are not getting any muted sounds with that, proceed to the 4 string version. Remember to strum only the strings that you fret and to mute the rest.
BTW, how old are you? You seem pretty sharp cos you are right about importance of developing your ear...
-- My current rig
Guitar: '98 MIJ Ibanez RG520 QS w EMG 81/60
Amp: Laney LC15R Tube, Fernandes 20W SS
Pedals: MI Audio Tube Zone Overdrive, Boss OD3, CS3, MT2, HM2, DS2, CE5, DD7, TU3, Beta Aivin DD2 Delay, Dunlop Crybaby 95Q, Stranger Vol Pedal, BBE SupaCharger
Others: Yamaha RBX 374 Bass, Yamaha MM-6 Synth, M-Audio Fast Track, Shure SM-57, Heet Sound E-Bow Plus
Wanted(pm if selling): EB VPJr/Boss FV500L,Ibanez w Original/Lo-Pro Edge