Go buy a larger external drive.
Basic Backup
For some people Time Machine will be more than adequate. Time Machine is part of OS X. There are two components:
1. A Time Machine preferences panel as part of System Preferences;
2. A Time Machine application located in the Applications folder. It is
used to manage backups and to restore backups. Time Machine
requires a backup drive that is at least twice the capacity of the
drive being backed up.
3. Time Machine requires a backup drive that is at least double the
capacity of the drive(s) it backs up.
Alternatively, get an external drive at least equal in size to the internal hard drive and make (and maintain) a bootable clone/backup. You can make a bootable clone using the Restore option of Disk Utility. You can also make and maintain clones with good backup software. My personal recommendations are (order is not significant):
1. Carbon Copy Cloner
2. Get Backup
3. Deja Vu
4. SuperDuper!
5. Synk Pro
6. Tri-Backup
Visit The XLab FAQs and read the FAQ on backup and restore. Also read How to Back Up and Restore Your Files. For help with using Time Machine visit Pondini's Time Machine FAQ for help with all things Time Machine.
Although you can buy a complete external drive system, you can also put one together if you are so inclined. It's relatively easy and only requires a Phillips head screwdriver (typically.) You can purchase hard drives separately. This gives you an opportunity to shop for the best prices on a hard drive of your choice. Reliable brands include Seagate, Hitachi, Western Digital, Toshiba, and Fujitsu. You can find reviews and benchmarks on many drives at Storage Review.
Enclosures for FireWire and USB are readily available. You can find only FireWire enclosures, only USB enclosures, and enclosures that feature multiple ports. I would stress getting enclosures that use the Oxford chipsets especially for Firewire drives (911, 921, 922, for example.) You can find enclosures at places such as;
1. Cool Drives
2. OWC
3. WiebeTech
4. Firewire Direct
5. California Drives
6. NewEgg
All you need do is remove a case cover, mount the hard drive in the enclosure and connect the cables, then re-attach the case cover. Usually the only tool required is a small or medium Phillips screwdriver.
Clone your MBP's drive to the external drive so you will have a bootable backup just in case. Here's how;
Clone using Restore Option of Disk Utility
1. Open Disk Utility in the Utilities folder.
2. Select the destination volume from the left side list.
3. Click on the Restore tab in the DU main window.
4. Select the destination volume from the left side list and drag
it to the Destination entry field.
5. Select the source volume from the left side list and drag it to
the Source entry field.
6. Double-check you got it right, then click on the Restore button.
Destination means the external backup drive. Source means the internal startup drive.
Before downloading and installing El Capitan do the following:
Repair the Hard Drive and Permissions
Boot from your Snow Leopard Installer disc. After the installer loads select your language and click on the Continue button. When the menu bar appears select Disk Utility from the Utilities menu. After DU loads select your hard drive entry (mfgr.'s ID and drive size) from the the left side list. In the DU status area you will see an entry for the S.M.A.R.T. status of the hard drive. If it does not say "Verified" then the hard drive is failing or failed. (SMART status is not reported on external Firewire or USB drives.) If the drive is "Verified" then select your OS X volume from the list on the left (sub-entry below the drive entry,) click on the First Aid tab, then click on the Repair Disk button. If DU reports any errors that have been fixed, then re-run Repair Disk until no errors are reported. If no errors are reported click on the Repair Permissions button. Wait until the operation completes, then quit DU and return to the installer.
If DU reports errors it cannot fix, then you will need Disk Warrior and/or Tech Tool Pro to repair the drive. If you don't have either of them or if neither of them can fix the drive, then you will need to reformat the drive and reinstall OS X.