My better summary (trollface):
Rick Grimes, a police officer in a small Georgia town, is shot during a gunfight with three violent criminals after being intercepted and wiping out during a car chase. He falls into a Coma, and awakens several weeks later to find his life support shut off and his IV drip nearly empty. He exits the room to find bullet holes, scorch marks, and rubble littering the hallway. He begins to leave the hospital and finds a door that is marked “DONT OPEN DEAD INSIDE”.
After leaving, he finds the hospital courtyard to be littered with dozens of bodies, all shot in the head and wrapped in sheets. Nearby is a small abandoned military encampment. He begins to panic, and goes back to his house, only to find that nobody is there and the surrounding houses have been looted.
He is sitting outside his house when a young boy sneaks up on him and knocks him out with a shovel. An older man – the boys father – approaches and takes Rick to his house after killing a Walker (zombie). They tie rick up to the bed because they think his gunshot wound may be a bite. After Rick explains that it isn’t a bite, he is released and allowed to roam the house. The man explains what has happened, and that there is supposed to be a refugee camp in Atlanta.
Rick takes them to the police station, where they load up on weapons and ammunition. The man explains to rick that he won’t be going with him to Atlanta until he teaches his son to shoot. He also secretly wants to put down his undead wife, who was bitten.
Rick leaves by himself in a squad car, and stops at a ranch when he runs out of fuel. The occupants have killed themselves, so Rick takes a horse and continues his journey. After reaching Atlanta, he finds the streets completely abandoned (apart from a few walkers), until he turns a corner and finds hundreds – if not thousands – of Walkers amassed in this street. He becomes surrounded next to a tank, and his horse eaten alive.
He crawls under the tank, and, after realizing that he won’t be able to escape, raises his gun to his head. As he looks up, he sees an open hatch on the belly of the tank and crawls in. Rick kills the undead soldier inside and takes his handgun and a grenade. After a short time, a voice comes onto the radio. “Hey, you. Dumbass, in the tank.” It turns out to be a small scouting group of survivors scavenging for supplies in the city. One of them tells Rick which way to run, and lets them into a building they are hiding in.
I’d type more, but I’m lazy. This gives a good description of the first episode and (I think most of) the second episode, maybe even the third. I can’t quite remember, honestly. It’s been a while since I watched season 1.