The Fallen Star
A star has fallen in New Tristram. Protect the town from the vile dead that have risen since it fell.

You start off at Overlook Road. This place reeks of death, the fallen star is near. To move, left click on a point in the ground.  Examine a sign, it says "Welcome to New Tristram".  Go to the east. Near a crashed wagon, you most likely will run into some undead risens. This is your first monster encounter. Use your left mouse button to attack them with your primary skill. Skills are the most effective way of killing monsters. These risens are pretty easy to beat, so do a quick practice of your combat powers. Test your secondary skill as well (right mouse button by default), which at this point is most likely just a melee attack. You can check the name and description of the skills by bringing up the skills menu ("S" by default). After beating these risens, keep heading east down the road, killing any enemy in your path.

When you arrive at the town, Captain Rumford is standing near the gate along with some guards. Notice he has a yellow exclamation mark on his head. Characters with that exclamation mark over their heads are quest givers. You can left click on them to speak to them.

DIablo 3 Captain Rumford

Speak to the captain. You tell him you seek the fallen star. Captain Rumford says that it fell on the old cathedral. There was only one survivor, Leah. You should speak with her.

The Tristram Militia warn Captaim Rumford that more dead are coming. You get a new objective:

Kill the risen dead attacking the gates

Objectives are phases you have to complete while doing a quest. This walkthrough, brought to you by rarityguide.com, will guide you on how to complete all the objectives. The current objectives appear under the minimap, or you can open your quest journal ("L") and read the description there. It can say something like:

The dead rise in the fires of the fallen star and descend upon New Tristram. Is this where my path has led me? IS this where I will find the understanding that I seek? Or is it my death that awaits me?

Captain Rumford and the guards cannot open the gates until they drive the risen back. Kill the Risens, who approach the town in waves. Captain Rumford is impressed by your fighting, he has never seen anyone fight like that before. He instructs his people to open the gates, and tells you that you will find Leah at the Slaughtered Calf Inn. This COMPLETES the objective of killing the Risens, and unlocks a new objective:

Talk to Leah in the Slaughtered Calf Inn

At this point you most likely get your first record (achievement):

Massacre
10 Monsters Killed
+20 XP Bonus

The gates are opened, and you reach Checkpoint. The Militia is burning the corpses in the meantime before they rise again. Explore this town, there are many NPCs, such as Brother Malachi the Healer who claims Zakarum has fallen to disgrace, and that no faith can save is, the end of the world is coming.

The Slaughtered Calf Inn is near the town square, NW of this big circle on the ground. There is a stash near the entrance, open it to find a minor health potion, which can be used to instantly restore some life. Right click on it to add it to your inventory. Enter the Inn and talk to Leah. She is standing near the bar, dressed in red, you should be able to identify her by the gold exclamation mark on top of her head, signifying she is a quest objective.

You ask her if she is Leah, and tell her that Rumford told you about how she survived the fallen star. Leah tells you she did survive, but it blasted her uncle, Deckard Cain, into the depths of the old cathedral. She tried and search for him, but the dead were already rising.  She came back here to rally the militia. She suddenly calls you to watch out, the wounded are turning. You get a new objective:

Kill the Risen

Kill the risen in the bar. Bron the Barkeep will be enthusiastic of your fighting and remark that this is killing business. Around this point you will be leveling up to level 2 and unlock a skill category, so be sure to choose a new skill. Skills are automatically added to your action bar. Also loot the corpses on the ground to get items or gold coins.

Talk to Leah again. She tells you that the dead will overwhelm you all unless something is done. You promise her that you will send them back to the graves and save her town. She thanks you and tells you that you should speak with Captain Rumford at the gate, he can tell you what to do.