I have come across the phrase 気をつけなければ but I do not understand how it works. Google translate says that it means "I have to be careful" but I can't find which conjugation it is using. To me it looks like the provisional form but I don't understand how that fits here. The full sentence is 両親を起こさないように気をつけなければならなかった.
V-nak-ereba is an abbreviation of V-nak-ereba naranai. The literal analysis of this is "if (-ba) I don't (-nai) [verb], it won't do (naranai)":
- 気をつける be careful.
- 気をつけない not be careful.
- 気をつけなければ… if they're not careful… (it won't do).
- 気をつけなければならない if they're not careful, it won't do (=they have to be careful).
Though that's the literal construction, the full expression is just the common, everyday way of saying "I have to [verb]", which is the idiomatic translation. Native speakers don't usually analyze its parts, just like English speakers don't usually think of breakfast as the interruption of fasting, etc.
しなければならない is one phrase. It means "must","have to". This ば don't have the meaning of supposition. You don't need to separate into 気をつけなければ and ならない.