Learn Russian: Наша семья дома.

Наша means "our" for feminine nouns. Because семья (family) ends in -я, it is a feminine noun. The possessive pronoun must match the gender of the noun it describes, so the masculine наш changes to the feminine наша.

Where is the word for "is" in this sentence?

In Russian, the present tense of the verb "to be" (am, is, are) is almost always skipped. The sentence literally translates to "Our family at home," which is the completely normal and correct way to say "Our family is at home."

Why does the word for home have an "a" at the end (дома instead of дом)?

The word дом means a physical "house." When you want to express the location of being "at home," you use the special fixed word дома.

What does the soft sign (ь) do in the word семья?

It acts as a separator. Instead of blending the consonant м directly into the vowel я, the soft sign creates a tiny split and a strong "y" sound. It makes the word sound like "sem-YA."