The Russian language is not that easier for Russians
Speaking the truth, Russians all the time confuse these two words! We often say "Я одела платье" instead of "Я надела платье", "Одень носки", when the right way to say that is "Надень носки". To be smarter than the Russians and to be able to correct them from time to time, REMEMBER that ОДЕТЬ + КОГО? (whom?)
НАДЕТЬ + ЧТО? (what?)
Here is a bit more explanation and examples
So, ОДЕТЬ must be use with people. It's like "to help somebody to get dressed". Like a child. Or a queen that never get dressed themselves and need assistance of maids;) For example:
Мама одевает сына на прогулку – Mom is helping her son to get dressed for a walk.
Девочка одела куклу и пошла с ней гулять – The girl got the doll dressed and went for a walk with it.
НАДЕТЬ we must use with object, with pieces of clothing like штаны, носки, платье, джинсы and etc. For example:
Надень свитер, здесь холодно. – Put on a sweater, it's cold in here.
Завтра на вечеринку я хочу надеть новое платье. – I want to put on my new dress for the party tomorrow.