Very simple method, just folow the steps:
Go to: About This Mac, click on the More Info button:
A new window will open. Now go to Software and check for: 64-bit Kernel and Extensions
See if its like in the image below:
If so, your machine is normally booting in 32Bit mode.
To test in 64Bit mode, just press and hold the keys 6 and 4 while booting. Beware that some Kernel apps might not work properly.
Go to Applications underneath Software and see what apps are ready for 64 Bit mode: