Learn Italian: Dammi il manuale, per favore. - Give me the manual, please.

Dammi is made by combining the informal command form of dare (to give), which is da', with the pronoun mi (to me). When you attach a pronoun to a short, one-syllable command like da', the first consonant of the pronoun doubles. That is why it becomes dammi instead of dami.

Is this a formal or informal way to ask for something?

This is informal, used with someone you address as tu. We know this because the pronoun attaches to the end of the verb in informal affirmative commands. If you were speaking formally (using Lei), the pronoun would go before the verb: Mi dia il manuale.

Does the consonant double with all pronouns attached to da'?

It doubles for most pronouns. For example, 'give us' is dacci and 'give it' is dallo. The only exception is the pronoun gli (to him or to them), which never doubles. So, 'give him' is simply dagli.

Why does manuale end in '-e' if it uses the masculine article il?