The best answer is read the PHB section on rogues, but the long and short of it is you get SA damage once per round when you have CA and hit with one of the listed weapons (light blade, sling, xbow, or sling). First Strike does give you CA, so it will allow sneak attack damage, but again only with the listed weapons, so no bows.
There are a few ways to get CA. First Strike is one. Flanking is another. Attacking when the enemy can't see you (IE you are hidden) is another. There are other ways too. A prone enemy grants CA (vs melee only), as does one which is dazed, stunned, surprised, restrained, or helpless. There are numerous powers and effects of various kinds that can grant CA under specific circumstances too, as well as some feats like Distant Advantage.
Its possible your DM might let you have SA damage with weapons not on the normal list, but that would be up to him to make a house rule. The main reason for the list is to keep rogues from getting SA damage with big heavy weapons and encourage them to use the light weight sneaky weapons that are more flavorful for a sneaky combatant. Crossbows I presume are on that list because they are a 'sniping' kind of weapon you can aim precisely. Who knows why slings are on the list, but they're not really a very good weapon overall so who cares. Bows probably aren't on the list simply because nobody would use a crossbow if they were.