The explanation of char is correct I think. I think this sentece means: You're going to get (a chance) to know someone and you'll become (a) friend/friends with them.

"I can get to know and get along well with people" 人 is person と is the particle and can mean if;when;and;with;and used for quoting. in this case i think it is with 知り合い (shiriau) is to get to know (someone), to make aquaintence. (or it can be used as a noun for an aquaintence). 仲良く (nakayoku) is to making friends with; getting along well with. できる has a few meanings, though in this case i guess it is to be able to/ can. I still have alot to learn about Japanese language though, so this could be totally wrong!!