Enter java -version on the command line. If it's 64-bits it will say so, otherwise it's 32-bits.
E.g.
64 bits Oracle / Mac OS X
$ java -version
java version "1.6.0_20"
Java(TM) SE Runtime Environment (build 1.6.0_20-b02-279-10M3065)
Java HotSpot(TM) 64-Bit Server VM (build 16.3-b01-279, mixed mode)
32 bits Oracle / Mac OS X (client)
$ java -version
java version "1.6.0_20"
Java(TM) SE Runtime Environment (build 1.6.0_20-b02-279-10M3065)
Java HotSpot(TM) Client VM (build 16.3-b01-279, mixed mode, sharing)
32 bits Oracle / Mac OS X (server)
$ java -server -version
java version "1.6.0_20"
Java(TM) SE Runtime Environment (build 1.6.0_20-b02-279-10M3065)
Java HotSpot(TM) Server VM (build 16.3-b01-279, mixed mode)
64 bits OpenJDK Ubuntu
$ java -version
java version "1.6.0_20"
OpenJDK Runtime Environment (IcedTea6 1.9.1) (6b20-1.9.1-1ubuntu3)
OpenJDK 64-Bit Server VM (build 17.0-b16, mixed mode)
32 bits Soylatte Mac OS X
$ java -version
java version "1.6.0_03-p3"
Java(TM) SE Runtime Environment (build 1.6.0_03-p3-landonf_19_aug_2008_14_55-b00)
Java HotSpot(TM) Client VM (build 1.6.0_03-p3-landonf_19_aug_2008_14_55-b00, mixed mode)
32 bits OpenJDK Mac OS X
$ java -version
openjdk version "1.6.0-internal"
OpenJDK Runtime Environment (build 1.6.0-internal-landonf_17_may_2009_13_58-b00)
OpenJDK Client VM (build 11.0-b17, mixed mode)
64 bits IBM Linux
$ java -version
java version "1.6.0"
Java(TM) SE Runtime Environment (build pxa6460sr8fp1-20100624_01(SR8 FP1))
IBM J9 VM (build 2.4, JRE 1.6.0 IBM J9 2.4 Linux amd64-64 jvmxa6460sr8ifx-20100609_59383 (JIT enabled, AOT enabled)