The short answer to your question is that the Agents have been tracking him for quite some time, along with various other "potentials" but they're not mandated to tackle redpills unless there's a compelling reason to do so. In-Matrix, the police can deal with low level hacking and nuisance.
Once he comes to the Agent's attention, it becomes apparent that Neo has a bulky file (complete with tracking photos and a scan of his passport) but it's not until Morpheus makes contact with Neo that the Agents start to show more than a passing interest in him. Had they known that he was "the one", Morpheus suggests that they would have simply killed him from the word 'go'.
Morpheus: This line is tapped, so I must be brief. They got to you first, but they've underestimated how important you are. If they
knew what I know, you'd probably be dead.
Neo: What are you talking about. What...what is happening to me?
Morpheus: You are the one, Neo. You see you may have spent the last few years looking for me, but I've spent my entire life looking
for you. Now do you still want to meet?
The sign that Neo is "the one" is pretty vague. An earlier version of the script suggests that Morpheus is actually a bit of a kook and that he's tagged other people as potential 'ones' in the past, all of whom have died while trying to confront Agents.
CYPHER : I'm going to let you in on a little secret here. Now don't
tell him I told you this, but this ain't the first time Morpheus
thought he found the One.
NEO : Really?
CYPHER : You bet your ass. It keeps him going. Maybe it keeps all
of us going.
NEO : How many were there?
CYPHER : Five. Since I've been here.
NEO : What happened to them?
CYPHER : Dead. All dead.
NEO : How?
CYPHER : Honestly? Morpheus. He got them all amped up believing in
bullshit. I watched each of them take on an agent and I watched each
of them die.Little piece of advice: you see an agent, you do what
we do; run. Run your ass off.
Morpheus does speak to how he knew where to look for Neo, the answer being that he spotted him in a chatroom and felt certain urges...
MORPHEUS : And then I saw you, on the Net, searching for me and everything changed. I felt this charge, this electricity through my
whole body. I started laughing and tears poured out of my eyes,
because I knew, I knew that you were the One.
