How can I repartition my hard drive?

I have a 2008 MacBook Pro, and last night, it suddenly restarted. When starting it again, it stayed on the grey screen with the Apple logo. Following a support page provided by Apple, I tried the following:

1. Start the Mac in safe mode

2. Reset the PRAM

To no avail. Then I restarted it, and held Command and R, and it went into disk utility. There, when Repairing my hard drive, Dis Utility told me to back-up the drive and repartition it.

I tried to back the disk up to a flash drive, but I got the error "The Source Could not be validated"

Then I proceeded to repartition the disk anyways, but I am confused on how to. I'm scared that if I erase the disk, Mac OSX will be gone, and I won't be able to use my computer.

I have two questions:

1. How can I backup my disk

2. How can I repartition it?