At Server A ( Source Database )

        RMAN> CONFIGURE CONTROLFILE AUTOBACKUP ON;

        RMAN>  backup database plus archivelog  ; 

Assuming : Full database backup is taken and copied to Server B 

At Server B ( Auxiliary Instance ): 

~~~~~~~~~~~~~~~~~~~~~~~

step:(1) sqlplus sys/syspwd@tnsmast112aux as sysdba

            ..

            Copyright (c) 1982, 2010, Oracle. All rights reserved.
            Connected to an idle instance.

           SQL> startup nomount 
                   ORACLE instance started.

                   Total System Global Area 363266048 bytes
                   Fixed Size 2253248 bytes
                   Variable Size 117444160 bytes
                   Database Buffers 239075328 bytes
                   Redo Buffers 4493312 bytes

step:(2) rman target sys/syspwd@tnsmast112aux
             ..
            connected to target database: MAST112 (not mounted)

step:(2a) RMAN> restore controlfile from 'F:\Share\C-3202207085-20131214-00';

               Starting restore at 14-DEC-13
               using target database control file instead of recovery catalog
               allocated channel: ORA_DISK_1
               channel ORA_DISK_1: SID=10 device type=DISK

               channel ORA_DISK_1: restoring control file

               channel ORA_DISK_1: restore complete, elapsed time: 00:00:03
               output file name=E:\ORADATA\M11202AUX\CTL\CONTROL01.CTL
               output file name=E:\ORADATA\M11202AUX\CTL\CONTROL02.CTL
               Finished restore at 14-DEC-13

step: (3) RMAN> alter database mount;
step: (4) RMAN> catalog start with 'F:\Share';

                      searching for all files that match the pattern F:\Share

                      List of Files Unknown to the Database
                      =====================================
                       File Name: F:\Share\C-3202207085-20131214-00
                       File Name: F:\Share\MAST112_1473_834142977_E1ORG0O1_1_1.BKP
                       File Name: F:\Share\MAST112_1474_834142979_E2ORG0O3_1_1.BKP
                       File Name: F:\Share\MAST112_1474_834142979_E2ORG0O3_2_1.BKP
                       File Name: F:\Share\MAST112_1475_834142979_E3ORG0O3_1_1.BKP
                       File Name: F:\Share\MAST112_1476_834142982_E4ORG0O6_1_1.BKP
                       File Name: F:\Share\MAST112_1477_834143079_E5ORG0R7_1_1.BKP

                       Do you really want to catalog the above files (enter YES or NO)? yes
                       cataloging files...
                       cataloging done

                       List of Cataloged Files
                       =======================
                       File Name: F:\Share\C-3202207085-20131214-00
                       File Name: F:\Share\MAST112_1473_834142977_E1ORG0O1_1_1.BKP
                       File Name: F:\Share\MAST112_1474_834142979_E2ORG0O3_1_1.BKP
                       File Name: F:\Share\MAST112_1474_834142979_E2ORG0O3_2_1.BKP
                       File Name: F:\Share\MAST112_1475_834142979_E3ORG0O3_1_1.BKP
                       File Name: F:\Share\MAST112_1476_834142982_E4ORG0O6_1_1.BKP
                       File Name: F:\Share\MAST112_1477_834143079_E5ORG0R7_1_1.BKP

step:(5): RMAN> run
{
allocate channel prmy1 type disk;
allocate channel prmy2 type disk;
allocate channel prmy3 type disk;
allocate channel prmy4 type disk;
SET NEWNAME for datafile 1 to 'E:\ORADATA\M11202AUX\DATA\SYSTEM01.DBF';
SET NEWNAME for datafile 2 to 'E:\ORADATA\M11202AUX\DATA\SYSAUX01.DBF';
SET NEWNAME for datafile 3 to 'E:\ORADATA\M11202AUX\DATA\UNDOTBS01.DBF';
SET NEWNAME for datafile 4 to 'E:\ORADATA\M11202AUX\DATA\USERS01.DBF';
SET NEWNAME for datafile 5 to 'E:\ORADATA\M11202AUX\DATA\DRPTBS01.DBF';
SET NEWNAME for tempfile 1 to 'E:\ORADATA\M11202AUX\DATA\TEMP01.DBF';
restore database;
switch datafile all;
}

output:
..
Finished restore at 14-DEC-13

datafile 1 switched to datafile copy
input datafile copy RECID=43 STAMP=834150521 file name=E:\ORADATA\M11202AUX\DATA\SYSTEM01.DBF
datafile 2 switched to datafile copy
input datafile copy RECID=44 STAMP=834150521 file name=E:\ORADATA\M11202AUX\DATA\SYSAUX01.DBF
datafile 3 switched to datafile copy
input datafile copy RECID=45 STAMP=834150521 file name=E:\ORADATA\M11202AUX\DATA\UNDOTBS01.DBF
datafile 4 switched to datafile copy
input datafile copy RECID=46 STAMP=834150522 file name=E:\ORADATA\M11202AUX\DATA\USERS01.DBF
datafile 5 switched to datafile copy
input datafile copy RECID=47 STAMP=834150522 file name=E:\ORADATA\M11202AUX\DATA\DRPTBS01.DBF
released channel: prmy1
released channel: prmy2
released channel: prmy3
released channel: prmy4

step:(6) SQL> shutdown immediate
                ..
              Database dismounted.
              ORACLE instance shut down.

step:(7) shutdown the source database at Server A, Copy the controlfile AND archivelogs AND REDO logs to Server B (cloned ) auxiliary instance

            Using OS command or winscp copy following files to Server B ( Auxiliary instance )

             *.ctl
             *.arc # Archivelogs is newly generated after backup at source database (Server A )
             REDO*.log

At Server B ( Auxiliary Instance ):

step:(8) Replace the auxiliary instance controlfile with newly copied controlfile

             Startup mount with new controlfile and catalog the archivelogs in any of below methods

             Sql> startup mount; # Auxiliary instance

              c:>rman target sys/syspwd@tnsmast112aux

              RMAN> CATALOG ARCHIVELOG 'F:\bkp\ARC0000000103_0828353631.0001';
              RMAN> CATALOG ARCHIVELOG 'F:\bkp\ARC0000000104_0828353631.0001';
               ..

                or

             RMAN> CATALOG start with 'F:\bkp\ARC*';

Step:(9) In this test case, Datafile, Redo location, Archivelog , Control location are NOT identical amount source database and destination database.
             So we need to rename Datafile and Redo file locatin

            SQL> alter database rename file '' to '';                       # do all for datafiles
               ..
               ..
            SQL> alter database rename file '' to '';   # do all for REDO logs

Step:(10) SQL > recover database ;
               SQL > alter database open;