Learn Russian: Это внучка дедушки. - This is the grandfather's granddaughter.

In English, we often use an apostrophe-s ("grandfather's granddaughter"). In Russian, possession is expressed using the Genitive case, which works more like the English word "of" ("the granddaughter of the grandfather"). Because of this, the owner (дедушки) comes right after the person or thing they own (внучка).

The dictionary word for grandfather is дедушка. Why does it end in -и here?

It is in the Genitive case to show possession. Normally, nouns ending in -а change their ending to -ы in the Genitive case. However, Russian has a strict spelling rule: you can never write the letter ы after к (and a few other letters like г and х). Instead, you must use и. That's why дедушка becomes дедушки.

Is дедушка a feminine word because it ends in -а?

No, it is masculine because it refers to a male person. However, it changes its endings exactly like a feminine noun! So while it takes feminine-style endings like -и here, any adjectives describing the grandfather would stay masculine.

Why isn't there a word for "is" in this sentence?