Expressing "Have to" or "Must"

There's a standard phrase used to express necessity or "must" for actions:

ければいけません
きゃいけません

The ければ version is more formal and found in written language, while the きゃ variant is more colloquial and can be found in casual speech. These phrases are added to the end of a negative plain form verb, after dropping the い in ない.

この飴を食べなければいけません。
この飴をたべなきゃいけません。
I have to eat this candy.

Though it sounds strange to have two negatives like that, what this essentially means is "you can't go without doing X", thus representing the "must do" or "have to do" that we have in English.

Because these phrases are painfully long and unwieldy, there are many other variants used in the spoken language. I'm going to list a couple of options for altering the phrases.

くちゃいけません
くてはいけません
いといけません

To make it even more casual, いけません can be dropped entirely, leaving something like:

学校に犬をつれてこなくちゃよ。
I have to bring my dog to school.

そのテストに勉強しないと。
I have to study for that test.

If the ければ or きゃ versions are used (rather than the ultra casual versions), なりません may sometimes replace the いけません portion.

毎日学校に行かなければなりません。
You must go to school every day.

いけません can also be altered as needed to indicate tense and politeness. The same is true for なりません, if it's used.

今朝七時に仕事に出なければいけませんでした。
I had to be to work at 7 this morning.

薬を飲まなくちゃいけない。
I have to take this medicine.

モールに服を買いに行かなきゃいけなかった。
I had to go to the mall to buy clothes.

There's a lot of variants to this phrase, but I think the most common one I've seen thus far is ~くちゃ, because it's far more casual and allows for ease of use. I'll have to read more to ensure I'm familiar with each of them.