To change database to archivelog or noarchivelog mode the database has to be in mount stage. If one tries to change the database to archivelog/noarchivelog during mount stage you will receive the following error message.

01:00:04 sys@TESTDB> alter database noarchivelog;
alter database noarchivelog
*
ERROR at line 1:
ORA-01507: database not mounted

Or if the database is open stage and trying to change Oracle will return the following error message.
00:59:01 sys@TESTDB> alter database noarchivelog;
alter database noarchivelog
*
ERROR at line 1:
ORA-01126: database must be mounted EXCLUSIVE and not open for this operation

To switch to noarchivelog mode
SQL> ALTER DATABASE NOARCHIVELOG;

Database altered.

To switch to archivelog mode (make sure archiver set to be running in this mode as if archiver process is not running, it would cause database to hang when switching archivelog file)
SQL> ALTER DATABASE ARCHIVELOG;

Database altered.

How to check if archiver is running