I'm a complete novice at Linux. I put my session on suspend, but when I tried to start it back up, it put me at the GRUB boot menu. After selecting Ubuntu, it put me in an initramfs prompt. I've tried looking for solutions but those required me to use live media or boot into Windows, neither of which I can do. My laptop is a Dell Inspiron 1420 and I have Ubuntu 15.10. What do I do? Thanks in advance.
Unfortunately, if your Ubuntu system won't boot, and you don't have any live media at hand, there isn't really anything you can do.
However, you could try booting into "Recovery mode" in GRUB (It's under Advanced Options), and see if that helps any.
If it doesn't, you'll need to get a hold of some live media. Then, you can reinstall Ubuntu (if the problem doesn't go away), or install Boot Repair (an application that fixes GRUB).