I don't really know how to explain it (but I'm sure other people will help you), but I can give you some examples :
Aussi can me "too", "as ..."
Me too -> Moi aussi
You are as strong as me -> Tu es aussi fort que moi
You have to do this and that -> Tu dois faire ceci et (aussi) cela (Aussi is not required here)
Ainsi can mean "just as" and "so"
So be it -> Ainsi soit-il
It's the way it is -> C'est ainsi
Just as I've already told you -> Ainsi que je t'ai déjà dit
Autant can mean "as much/many, so much/many"
Eat as much as you want. - Mange autant que tu veux