update FieldTripList
set FieldTripTeacher = s.CurrentTeacher
from Student s
where fk_StudentID = s.StudentID
More generic example with joining away to two tables: update columns in [TableA], by joining to [TableB] and [TableC] and using the values from those tables
update [TableA]
set TableAValueB = TableBValue,
TableAValueC = TableCValue
from [TableB], [TableC]
where TableAID = TableBID
and TableBID = TableCID