Backup by burning to a CD or DVD, copy or backup to an external hard drive or, for a small amount, to a flash drive.
[Edit: Ah, I didn't see lapprincess' post before I posted.]
A replacement drive does not need to be a Gateway. In fact, your current drive is probably not made by Gateway; I don't believe Gateway makes hard drives. The major hard drive makers are Western Digital, Seagate, FUJITSU, Hitachi, etc., as you can see at
Notebook, / Laptop Hard Drives Deals, from newegg.com. If you look elsewhere, be sure to get a 2.5 inch hard drive, since you have a laptop. Desktop computers use 3.5 inch hard drives.
Even though you computer may appear to be running normal, if you see that warning everytime you start, again, take it very seriously and be prepared for a total hard drive failure to occur at any time.