On PC, hitting F or numpad+ twice highlights the status bar and you can figure out the name of each effect.
After that, it gets tricky because you'll need to look up the effects online somewhere. You might a lot of these effects (Berserk, Paralyze, Slow) are self explanatory, but the potency of these effects can vary, so it's not always clear, even to veterans.
Food effects, check out ffxiah.com or http://wiki.ffxiclopedia.org/wiki/Main_Page and find your food. The effects should be listed there.
All of this is a bit of a hassle, but the game is 10 years old and standards were different back then. SE is working on an upgrade to the UI, but a lot of the details are still secret to us.