Learn Russian: Здравствуйте, это мой учитель.

Russian has some words with heavy consonant groups where one letter is dropped in speech to make it easier to pronounce. In Здравствуйте, the first в is completely silent.

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

Russian does not use a verb for "is", "am", or "are" in the present tense. To say "this is my teacher", you simply place the words side by side like "this my teacher" (это мой учитель).

Why doesn't the word это change to match the masculine gender of учитель?

When you use это to mean "this is" to introduce someone or something, it acts as a fixed pointing word. It always stays in this default form, regardless of the gender or number of the noun that comes after it.

The word учитель ends in a soft sign (ь). How do I know its gender?

Nouns ending in a soft sign can be either masculine or feminine. In this sentence, you can tell учитель is masculine because it uses the masculine word for "my", which is мой. A female teacher would be учительница, which pairs with the feminine моя.