The only people admitted on the floor of the House Chamber are members of the House and Senate, constitutional officers, ex-governors of Minnesota, judges of the Trial and Appellate Courts, members of Congress, members of the press, and House staff. The House rules note that a "family member of a member" is also allowed. In addition, some allowances are made for special visitors to go onto the House floor. The House rules contains a complete list of those admitted.
See also the FAQ: Are visitors allowed to attend sessions of the Senate and House?