"I don't have an idea" means something different from "I have no idea". The former might be used when someone has asked you or a group of people for their ideas on some topic and you have replied that you do not have one. The latter means that you are completely ignorant (or clueless) about something. The first can be translated literally whereas the second is an idiomatic expression. So I think the translation of your sentence would be literally something like "ich habe keine Idee"
You use a different verb form based on what the subject of the sentence is. Similarly in English, we say "I have" but "He has" or even "I am / You are / He is."
So in German: "ich habe | du hast | er/sie/es hat | wir haben | ihr habt | sie/Sie haben."
"Haben" is a very irregular verb, but most verbs will follow a specific pattern of putting these endings on the verb: "ich spiele | du spielst | er/sie/es spielt | wir spielen | ihr spielt | sie/Sie spielen."