Use is the man (or you're the man) to praise someone who just did something impressive, in casual speech between people who know each other. Nice work fixing the sink, you're the man.
A teammate nails the presentation: He's the man! A friendly, spoken compliment.
Same words, different job: He is the man I met yesterday. That's literal identification, not praise, so the idiom meaning doesn't apply.
When a friend pulls it off
Your friend fixes your laptop in five minutes: You're the man! That fits casual speech between people who know each other, right after the impressive thing happened.
A coworker covers your shift without being asked: You're the man, thanks for covering my shift. Praise like this works when you're talking to teammates in person, not writing a report.
Talking about him to someone else? Use the third-person form: He's the man! Same casual, spoken setting, just aimed at a person who isn't listening.
Contrast: a job interview. You wouldn't tell the panel My reference is the man. In formal or written settings the idiom sounds out of place, so save it for relaxed, spoken moments.
When someone else is needed for the job
The man can also point to the right person for a particular task. When you say someone is the man in this sense, you're naming him as the one who can handle the job at hand. That's the reading behind a line like If the car won't start, Dave's the man.
The man works in two closely related ways. Its usual job is casual praise for a recent achievement: someone just did something impressive, and you say it out loud. Sometimes the man also means the person needed for the job, not just someone you admire. If the car won't start, Dave's the man. Here you're pointing to him as the right person to fix it, an extension of the praise rather than a separate phrase.
Use this sense when you're recommending someone for a task. Ask Joe about the wiring, he's the man for that. The praise is attached to a specific job rather than a recent achievement, so add for plus the task when it helps your listener.
The job sense often shows up as he's the man for the job, so that's the safest spoken form. It's slang, which usually lives in speech rather than writing, so keep it in conversation.
One boundary to remember: don't reach for the idiom when you're introducing someone formally. This is the man who fixed our servers is plain identification, so the idiomatic praise doesn't apply there.