Learn Russian: Это сестра.

In the nominative case (the basic dictionary form of a word), you can usually guess a noun's gender by its last letter. Words ending in -а or -я, like сестра, are almost always feminine.

If сестра is feminine, why do we use это, which looks like a neuter word?

When это is used to mean 'This is...' to introduce something, it acts as a fixed starting word. It doesn't change to match the gender of the noun. You would only change it to the feminine эта if you were saying 'this sister' as a single phrase instead of 'This is a sister.'

Why aren't there words for 'is' or 'a' in the Russian sentence?

Russian does not have translations for articles like 'a' or 'the.' Also, in the present tense, the verb 'to be' (is/am/are) is almost always dropped. That is why 'This is a sister' translates to just two words: Это сестра.