I’m not sure there is a “rule” because both could be correct but one will always sounds more natural than the other depending on your phrase. I’ve maybe find a way to know wich one to use.
Try to ask the questions de quoi ? and quoi ? instead of the word where you have a doubt.

For examples :

J'ai besoin de plus d'expérience -> j'ai besoin "de quoi" ? – you ask "de quoi" so you use "d'". However Il me faut de l'aide -> Il me faut "quoi" ? – you ask "quoi" so you use "de".

I’m not sure it works every time but it may help you to understand when you use “de” or “d'”

Hope I’ve help you !

The usual form would be the ones without the article:

Tu as besoin d’aide: you need help

Tu as besoin d’expérience: you need (to have some) experience

You would use the form with an article when the complement is defined:

Tu as besoin de l’aide de ton professeur: you need your teacher’s help

Tu as besoin de l’expérience d’un vieux routier: you need the know-how of an old-timer.