The first thing I'd do would be to clean and lube the rear derailleur cable. Start by shifting up to the biggest cog in the back. Then without turning the pedals, shift towards the smaller cogs. This should allow the cable to go slack. Check the cable guide under the bottom bracket for dirt, dried-up worms, Gatorade residue, etc. Clean the guide and the cable then lube it with some light oil. I like using a teflon-based lube.

Next go to the rear derailleur and gently pull out the cable housing from the chain stay holder. There should be a split in the holder to allow this. Slide the cable housing to expose the cable. Clean and lube the cable.

While your there, spray some lube into the pivot pins on the rear derailleur.

Put everything back together and shift up towards the largest cog again.

IMPORTANT: Make sure that the cable is in properly the guide under the bottom bracket.