Learn Russian: Ей почти два года.

In Russian, you don't say that a person is a certain age. Instead, you use the Dative case, which is like saying "to" or "for" someone. Here, ей is the Dative form of "she" and means "to her", making the sentence literally "To her [are] almost two years."

Why is the word for years года here instead of год or лет?

The Russian word for "year" changes depending on the number right before it. After the numbers 2, 3, and 4, you must use the Genitive singular form, which is года. If the number were 1, you would use год, and for 5 through 20 you would use лет.

Since we are talking about a female, why do we use два instead of the feminine form две?

Numbers match the gender of the thing being counted, not the person you are talking about. Here, we are counting years. The Russian word for year (год) is masculine, so we must use the masculine number два regardless of whose age it is.

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

Russian routinely drops the verb "to be" in the present tense. The literal structure is just "To her almost two years." If you wanted to talk about the past ("She was almost two"), you would add the past tense verb было.