As with just about every other issue, how you relate to this person is more about you than about them. There will always be people who don't pull their own weight in a given work environment for a variety of reasons. First and foremost, you really need to make sure that your gripes are because you are being regularly blocked by them, for example, or if you're just peeved that you seem to do a lot more work than they do. If it's the latter, I would propose not doing anything about the situation and instead learn how to deal with this issue internally.
If it is the former, you can try going to them but it's often hard to have a face to face discussion with a peer about stuff like this. If you do, it is imperative that you use "I" statements ("I was unable do complete a task yesterday because Document XYZ was not filled out" instead of "you need to fill out Document XYZ") and, really, not be straight up accusatory. The "this guy is lazy" thing especially is at its root an accusation. Even if you know in your heart that the root cause is this guy's laziness, you ought to be prepared for the chance that you're seeing things incorrectly.
I also wouldn't go the route of asking about their personal business unless you are really and truly interested in their well-being. That kind of thing is hard to fake and if you go up asking how someone is doing in an insincere way, chances are they will notice it straight away. Instead, keep things on the business end and if they proffer an excuse that is personal, try to address it in business terms ("Okay, so you're going through a messy divorce and have to be out of the office by 4? Can you make sure that Document XYZ is completed by 3, then? If you can do that, I can know that I have to get all of my stuff done before that time"). On the flip side, that also means you shouldn't include personal stuff in your criticism of him. "My work is being affected by your not hitting deadlines" is professional; "I feel frustrated that you are not working as hard as I am" is personal and likely to be taken as an insult.
Otherwise, if you'd prefer to go to your supervisor, and I would not blame you if you did, you need to make sure it's not just a gossip/gripe session. Continue to present things as "I" statements (if you feel like that is overly clingy, well, don't worry about that - others will attribute bad statements to you whether you say them as "I" statements or as "they" statements) so as to make your boss understand the personal impact this person's laziness is having on the workplace. Be open to alternatives, and as mentioned in the first paragraph being peeved that a colleague isn't pulling their weight isn't really reason enough in and of itself for your boss to intercede on your behalf.