Be aware of power usage on new drive
I recently upgraded the hard drives on both an older and newer MacBook with no issues. The Apple support web site has DIY pages to walk you through the process of removing and installing the hard drive for your specific model. I used Carbon Copy Cloner to duplicate the existing drive to the new drive using a cheap USB to SATA adapter, then swapped the drives. Choose a hard drive with similar power requirements of your existing drive, so you don't adversely affect your battery life. I used the Fujitsu 500 GB (5400 RPM), which uses less power than their 320 GB drive.