"I.e." is an abbreviation for the Latin words "'id est." It means "in other words" (i.e., "That is"). It is a RESTATEMENT or a CLARIFICATION. For example: I'm going to my favorite room in the house (i.e., my bedroom). For a silly mnuemonic, think of "i.e." as "in ether words." Wrong, yes, but memorable!
"E.g." means something else entirely. It is an abbreviation of the Latin words "exemply gratia," which means "for the sake of example" or "including." For example: I have many rooms in my house (e.g., kitchen, guest room, bathrooms). Those are simply EXAMPLES of the rooms in my house. Another silly mneumonic would be "examples, good." Do not use "etc." at the end of your examples. It is an abbrevation for the Latin word, "et cetera," which means, "and other things." It is redundant if you have used "e.g."