Learn Russian: Это не ночь, это день.

Nouns ending in a soft sign can be either masculine or feminine. Unfortunately, there is no strict rule, so you just have to memorize their gender when you learn them! Here, день is masculine, and ночь is feminine. (Bonus tip: Any noun ending in -чь, like ночь, is always feminine).

What does the soft sign (ь) actually do to the pronunciation of these words?

The soft sign doesn't make a sound of its own. Instead, it makes the consonant right before it "soft" (meaning you raise the middle of your tongue toward the roof of your mouth). In день, it softens the н. The ч in ночь is already always soft in Russian, so the soft sign there is mostly a spelling rule to show that it's a feminine noun.

Why is there no word for "is" in this sentence?

In Russian, the present tense of the verb "to be" (am, is, are) is almost always skipped. The word это acts as "this" or "this is". So, это день literally translates to "this day", but it is understood as "this is day".

Why do we use не for "not" instead of нет?

Нет means the standalone word "no" (the opposite of "yes"). Не means "not" and is used to negate the specific word that comes right after it. Since we are saying it is not night, we put не directly in front of ночь.