The _grammatically_ correct way to say this would be “I and my friends” – it is the subject of the sentence here, so there is no reason to put “I” into the objective case. As others mentioned in their answers “My friends and I” would be more common, but both are equally grammatically correct.
Technically, strictly speaking, formally, “Me and my friends” is incorrect, BUT native speakers will say this all the time, so if you are not taking a grammar test, but rather just speaking in the real world, you’ll be fine.
Here is why this happens. For all kinds of weird reasons, the objective case of personal pronouns became the default one in sentences without a verb. For example:
— Who wants to go to the cinema?
— Me!
There is no reason to use “I” in the objective case here, it would be correct to say “I!”, but virtually no one does this. Now, in your example there is a verb, so:
— Me decided to go to the cinema. (WRONG)
is entirely incorrect.
— I decided to go to the cinema.
is the only possible way of saying this. But! As you add your friends, the subject of the sentence becomes “conjoined” and, intuitively, the pronoun moves further from the verb and kinda-sorta “loses sight” of it and therefore tends to switch to the objective:
— Me and my friends decided to go to the cinema. (Not 100% correct grammatically, but native speakers will say this.)