One of my most terrifying moments as a pilot: the first time I went to the local practice field in a plane with TCAS.
You won't see all traffic: it's impossible. A little white plane on the horizon can be a real pain to see, and replacing the horizon with clouds or visually busy urban areas doesn't help, either. Just keep your scan up and hopefully it will appear. If you're on with control/tower and it's not too busy, let them know you still can't see the traffic and they'll update you on its position and give you instructions to stay clear, if necessary.
Not to scare you, but the closest I've ever come to a mid-air was on a beautiful VFR day with flight following. A Mooney and me, head-on, both on frequency. ATC gave us a traffic advisory about five seconds after we passed. We probably would have missed by about 150 feet, but we saw one another beforehand and made our right banks clear. Point being: I'm more concerned about the traffic ATC isn't telling me about than that it is. A corollary: don't totally fixate on trying to find the traffic ATC is calling; they may not see the plane right in front of you, either.