I worked with one of those search teams BrotherWu mentioned once. I volunteered to spend a saturday beating the brush through a national forest. I learned a few things.
1. There are cadaver dogs, live find dogs, and a third kind that I can't remember right now. The dogs cannot be cross trained effectively.
2. Sometimes people who have one kind have others, but they don't bring more than one type because you work them differently.
3. Like BrotherWu said, there are groups who do this, get in contact with them, and if they've already been contacted, try to be there to help just to see how they work. They will always welcome volunteers. They might have reservations with you knowing the person, but if they do, then lie. Or hang around anyway and bring water to the volunteers. I know the group in my area but I don't know how to find others.
4. If it's not an emergency and can be planned for a weekend, you get a huge turnout. People with those dogs jump at the chance to get some work in. The time I did it, I can't even tell you how many dog teams we had, but they came from far away. I think some came from out of state. They told me if it hadn't been planned a week in advance, we would have likely only had one team.
5. Success is not guaranteed. For the one I did, the guy had been missing for over a month. The only reason they reopened it was because a hiker found his backpack with ID in a part of the forest they hadn't checked very well. When I asked the regulars what the odds were, they mostly just shook their heads. I think the only number I got was 1% because of how old it was. BrotherWu might be able to tell you more realistic odds for one as recent as yours.
1. The three types area "Area Search", "Human Remains" and "Trailing". Area search is just like it sounds. They work off lead and can find, any person in the area, a specific person in an area, or a "large source" of human remains. HR dogs also work off lead and can find "Small Source" such as bone fragments, teeth, etc. Trailing dogs work on a lead and don't "air scent". They pick up scent directly off the ground. If you know a last-known position, they're usually the first type of dog used to establish a direction of travel.
2. If you don't have a last known position or a direction of travel but think they are in an area, you can break the area into sectors and work it with area search dogs. Usually a team will be at least one handler and 1-2 field support working the dog in a grid according to wind conditions, support working coms, navigating the sector, keeping the dog safe, etc.
3. More than likely, they would not welcome you on an active search regardless. For our teams, at least, there is quite a bit of training to be completed, background checks, etc. until you are on a callout. About 6 months to a year of training.
4. In MI, I have seen 10-15 dog teams on searches. Doesn't matter if it is a weekend, weekday, day or night. They'll show up.
5. Depends on the terrain and how clever or lost they are. If you find his vehicle within a day or two, chances are pretty good. I'd say 75%+ on the first day. The longer it goes before you start, it drops off some because you lose the original trail and then you're just using a process of elimination.
Sometimes, before starting any of this shit, you do a "hasty search" within a perimeter of the LKP. Maybe a couple hundred meters.
Good luck.