When you pick this race, choose a race that you were in life. This affects your physical body, as well as your traits. A tiefling, for example, would have bone horns and a tail, as well as it's respective traits. You keep all of your base race's traits other than those below that would replace former traits, and gain all other traits listed below.

You gain all the ability score improvements from your former life (add them manually).

Your undead nature grants you an indefinite lifespan. 

Skeletons tend towards their former alignments, though death can sometimes twist them towards evil.

Skeletons retain the size they had in life, losing a few in inches to decomposition.

Your base walking speed is the same as it was in your former life.

A skeleton doesn't require air, food, drink, or sleep, but to regain spell slots, traits, and similar things, you spend the duration of the long or short rest doing no more than light work.

Your lack of flesh grants you an immunity to poison damage, as well as an immunity to being poisoned.

Skeletons are not buoyant, having lost their flesh, and sink in water. They do not need to breathe, however, and could simply traverse the bed of a river to get to the other side while their companions swim over.

With no flesh to guard bone, you have a vulnerability to bludgeoning damage, but with no flesh to pierce or blood to lose, you gain a resistance to piercing damage.

You can read, write, and understand all languages you knew in life, and by some mysterious magic, you can speak.