There might be other ways, but if I were to do it, here is what would come to mind:
Buy an external enclosure for your new hd. (Do a search on Google for "osx external notebook drive enclosure" and a few will pop up.) Install your new internal hard drive into the enclosure. Plug your new hard drive into your compatible Firewire or USB connection and setup it up as an external hard drive that appears on your MacBook.
Assuming that you have one partition currently on your internal hard drive and want to copy everything, divide your external hard drive into two partitions. Make the first one the exact same size as your original 60 gb hd and then make the second partition with whatever disk space is remaining. Download and install SuperDuper (a disk backup and cloning tool -
http://www.shirt-pocket.com/SuperDuper/). Use it to create an exact bootable copy of your current internal hard drive on the external partition that is set up to be the same size.
Once all the files are copied, setup your MacBook to boot up from the external partition in your System Preferences / Startup Disk to test it. Then reboot the laptop, and see if it starts up from the external partition which is a clone of the internal hard drive.
If all seems to be o.k., then switch out the current internal hard drive, and place the new hard drive from the external enclosure into your laptop. Boot up, and it should work. And now with the external enclosure, your original hard drive can be used as for backup purposes!
Might need to do a little research on which enclosure to get and the SuperDuper software, but this should give you the overall steps involved. I hope this helps.