How does a mountain racing team work together?
Each type of racing is able to take advantage of certain team dynamics, and a few things are common across all disciplines.

Specifics:


DH/Super D: Downhill "teams" are more associated by sponsors and bikes than by riding together during a race. Since each run is done one at a time there's no drafting or anything like that. However, during track walks and practice teammates can help each other with line choice and bike setup suggestions.
XC/Marathon/Cyclocross: Cross country teams sometimes act more like a road team with drafting happening on straights and doubletrack sections. Teammates can also help pace each other through longer races. With teams that have riders across multiple levels of competition or age groups, some team members may act as support during another member's race (hand ups, mechanical, etc.).
Enduro: Though relatively new as a competition (in some parts of the world), Enduro takes facets from both XC and DH. Typical Enduro races are one at a time affairs where each rider is on his own, but might benefit from teammates during practice like a DH race. However, in races like the Megavalanche with a mass start, teammates can help to protect each other or advance a rider through a pack.
Other: 4X is pretty similar to BMX and DH in that practice usually assists the teammate more than during the race. Trials is the same. Short track is closer to road and XC in team dynamics, but more like a Criterium in pace and tactics.


Shared:


Training(Bike): Most teams have at least a few training sessions as a whole team. Obviously this can be difficult logistically if team members are further apart (other side of the country/world/state). Sometimes this takes the form of special trips, such as to an area of high altitude, for working on specific training. Other times it's just regular rides or skills work.
Training(Other): Large teams have associations with gyms an trainers to provide their athletes with good off-bike training as well. Team workouts happen along with individual workouts tailored for the rider's needs.
Nutrition: Again, larger teams usually benefit more here with a dedicated health person who will work with the athletes on their nutrition and food intake.
Race support: Mechanics, cheering, pits and everything else that happens on race day is supported by everyone on the team. Whether that's a teammate on the sidelines cheering you on up a grueling climb, or your mechanic making that last minute suspension change before your finals run.


Ultimately, a team is what you make of it. I know guys who ride for a team, but are pretty solitary and keep to themselves. There are other teams that seem more like a traveling party, but they know when to train and when to have fun!