"I needn't to" is not actually correct English. However, you can say "I needn't" +infinitive verb, or "I didn't need to"+ infinitive.
"I needn't" means it is not necessary for me to do something in the present or future. Eg you could say "My husband has just bought some milk, so now I needn't go to the shops."
"I didn't need to" has the same meaning but refers to the past, eg "I didn't need to go to the shops yesterday, because my husband had already bought some milk."
"I needn't have" is different from "I didn't need to." This implies that you completed the action and afterwards found that it wasn't necessary. Eg "I went to the shop and bought some milk. When I got home, I found that my husband had already bought some, so...I needn't have gone."
"I needn't" means it is not necessary for me to do something in the present or future. Eg you could say "My husband has just bought some milk, so now I needn't go to the shops."
"I didn't need to" has the same meaning but refers to the past, eg "I didn't need to go to the shops yesterday, because my husband had already bought some milk."
"I needn't have" is different from "I didn't need to." This implies that you completed the action and afterwards found that it wasn't necessary. Eg "I went to the shop and bought some milk. When I got home, I found that my husband had already bought some, so...I needn't have gone."
