Learn Spanish (Spain): Es el perro del vecino.

Spanish doesn't have an apostrophe 's to show possession. Instead, you always use the preposition de (of) and flip the word order. "The neighbor's dog" literally becomes "the dog of the neighbor" (el perro de...).

Where does the word del come from?

del is a required contraction. Whenever the word de (of) is directly followed by the masculine word for "the" (el), they combine into one word: del. So, de + el vecino becomes del vecino.

If the neighbor were a woman, would it still use del?

No, it would be de la vecina. The contraction del only happens with the masculine el. For feminine words, you keep the words separate.

Why does the sentence start directly with Es? Where is the word for "It"?

Spanish often drops subject words like "it", "he", or "she" because the verb itself gives enough information. Here, the verb Es means "It is" all on its own.