Much like てはいけない, なくてはいけない states that something ‘must not’ be done. However, this is where the similarities end. なくてはいけない is an example of a double negative in Japanese, and actually has the meaning ‘(A) must be done’, or ‘must do (A)’.
While this grammar point is usually translated as ‘must do’, the literal translation is ‘must not, not do (A)’. This double ‘not’ is where many learners have difficulties. いけない simply means ‘cannot go’, and comes from the negative potential form of 行（い）く.
To use this structure, simply create the negative form of a verb, and then convert ない to なく (the conjunctive form of an い-Adjective), followed by て. After this, は is added, and then finally いけない.

• 今日（きょう）は９時（じ）に寝（ね）なくてはいけない。
  Today, I must sleep at 9. (I must not, not do it)
• 明日（あした）は彼女（かのじょ）の誕生日（たんじょうび）プレゼントを買（か）わなくてはいけない。
  I must buy my girlfriend's birthday present tomorrow. (I must not, not do it)
• 明日（あした）は友達（ともだち）が来（く）るから、家（いえ）の掃除（そうじ）をしなくてはいけない。
  Since my friend is coming tomorrow, I must clean my house. (I must not, not do it)

いけない is considered to be the most common structure used with the ‘must’, and ‘must not’ grammar points, and is natural in both speech, and written Japanese. Alternatively, ならない may be used in formal speech, but is much better suited to writing. だめ is also acceptable, but much more casual than either いけない or ならない.

• 朝食後（ちょうしょくご）に薬（くすり）を飲（の）まなくてはならない。
  After breakfast, I must drink my medicine.
• 野菜（やさい）も食（た）べなくてはダメだよ。
  You must also eat vegetables.