Independent characters can only be chosen as targets if they are more than 6" away from any other viable target unit or if they are the closest target at short range (up to 12"). Otherwise you can't shoot at them.
Characters shoot just like ordinary troopers, although in many cases they will have superior Ballistic Skills or exotic weaponry that sets them apart. Where this is the case either roll for them separately or use different coloured dice to differentiate their shooting.
Errata — Chapter Approved: Main Rules Clarifications (v2.0): You can't shoot at an Independent Character if he's within 6" of a unit (even if it's a vehicle and he's not), unless he's the closest model at short range (12" or less). If he has joined a unit you may not shoot at him even if he is the closest model within short range.
Errata — Chapter Approved: Main Rules Clarifications (v2.0): When shooting at a character (see page 75 of the Warhammer 40,000 rule book) a viable target is deemed to be one that the firing unit has at least one ranged weapon capable of wounding or scoring a glancing hit against.