To do an assignment in Queue (either of an ad hoc task or a standard task) look for the current assignment. This should be next to the Work It or Grab It button.
Click on this to select the individual or team you wish.
Be sure to select the individual within the correct team. Also, if you wish to assign it to the team without selecting an individual, select Unassigned within that team.
Note the type-ahead functionality. This can be a good way to limit a large list of teams or people. This will dynamically limit to teams (with all the people within them) and individuals that match the string provided.