Starting after you kill the tree boss:
Head down to the tower where the giant is shooting arrows. If you leave the tree boss room from the main door, the pathway is to the left. There are lots of pot guys and whatnot.
Go down the elevator, and you will come to a valley. Progress through that and you will come to a marsh/forest looking area.
From here you can either kill the area boss, by going left when you get to the bottom after the bonfire with the two knights, or head to the poison swamp by looking for the big door with the two people guarding it.
Heading left will lead you to the boss, and then after that it is a linear progression up to the Cathedral of the Deep. You need to kill the Deacons here in order to progress later.
If you go to the poison swamp, you will need to extinguish some pillars. I recommend following the fires in order to stay in the shallow water. Once extinguished, a door will open up that leads to the first Lord of Cinder boss.
The next area (The Catacombs) is linear in progression. After the boss, you will be in the Boreal Valley. From this area you can find Pontiff Sulyvahn and forge onwards to another Lord of Cinder. Near the shallow water with the long haired spider ladies, you should hug the left wall and you will see an opening. This is the way to the Pontiff.
Alternatively, you can head to the sewers/prison which can be found near the shallow water with the long haired spider ladies. Following this is also a linear progression up until the next Lord of Cinder.
After you've killed three Lords of Cinder, you can progress deeper into Lothric by going back to the room where the woman sits. The woman who gave you the banner at the start. You can't really get lost from here.