The Fallen Star
Kill the Wretched Queen and the Wretched Mothers in the Old Ruins northeast of New Tristram
The wretched mothers and their queen call forth more of the Zombies. If I kill these leaders, New Tristram should be safe from their attacks. At least for a short while.
After talking to Captain Rumford, take the road northeast from the gates of New Tristram. Cross a bridge and some stairs to arrive at Old Tristram Road. Along the road you are sure to encounter Undead such as Risen and Walking Corpses, and beasts such as Quill Fiends. If you get injured, make sure to left click on a potion to replenish your life. Health Potions can be assigned to your action bar from your inventory. At this level you probably have minor health potions.
Look out for red dots on your minimap. The red dot on your mini-map points to a monster that you need to kill for a quest, in this case, either the Wretched Mothers or the Wretched Queen. Pick up any items that monsters drop, such as a Thick Sash or a Hand Axe, or some gold. Even if you don't need an item, you can always sell it later to a merchant.
Near a burnt down wagon on the side of the road there is a body of a Dead Tristram Militia. Search it for loot, then continue northeast along the path. If you see a Tree Stump, attack it to reveal some loot, usually in the form of gold coins.
There will also be some optional environments to explore. Enter a Musty Cellar if you find one. Loot the body of dead plunderers laying on the floor, and search the cellars for treasure. Attack barrels to break them, and perhaps find gold or equipment inside. Exit the cellar once you are done exploring it.
Keep working your way towards the north/north east. When you reach the corner, the road turns east. Keep following it, until you reach The Old Ruins. Note the yellow circle on the minimap, which marks the quest destination, as well as the red dot which shows the location of the Wretched Queen, first handmaiden of the Queen. Note that her name appears in purple, meaning she is a super unique monster or a boss. Fighting her will be harder then the monsters you have fought so far. Her attacks are more powerful, and she sends Risens at you. She also has a lot more health then the normal monsters. Defeat the Wretched Queen.