The Shadowitz group knacks represent particular edges that a shadowruner team's orientation grants them. For example, one team template is Corporate Backed. These runners are in the employ of one of the megacorporations, housed in corporate housing, trained by corporate experts, equipped from corporate supplies, etc. They are effectively owned by the corporation, as they exist off the record, thus allowing the corp to claim plausible denaibility should they ever be captured. However, as compensation, the team gets the knack Requisition, which functions as a team Resources knack with a much bigger bank account.
The Street Trash team is more like what you actually wind up with in a Shadowrun game, at least in my experience. It's a bunch of independent criminals, all relatively low scale, some with records or with a history of trouble with some organization (law enforcement or otherwise), all with skeletons in their closets. The group tends to be violent and crude, but gets the job done. This team template gets the knack Bolt Hole. With each team member used to being in trouble, it's assumed everyone maintains some kind of crash house somewhere, and when the drek hits the fan, the team can roll this knack to find one of those places. Hits are divvied up between the lifestyle and security of said hole (and it probably will be a hole, at least to start).
Each team has its own knack and method rating for its special knack. Increasing these is just like increasing a knack or method on your individual character sheet. It uses the same formula to figure the experience cost. However, that cost must be paid in full by every single member of the team. If one person doesn't pay, you can't buy up the score. It's a team. Everyone's in or it doesn't go.