Cemetery of Ash
This is the tutorial area of the game. Read the tutorial messages on the ground, learn the basic of melee combat, explore the area, and grab all items. Defeat all enemies in the area. However, there is a path leading to a mini-boss, i.e. a Ravenous Crystal Lizard, that should be left alone for now. Later in the game when your character and weapon are stronger, you can return to the area to fight the mini-boss. Near the entrance to the tutorial boss, i.e. Iudex Gundyr, are 5 Firebombs that are useful during the second phase of the boss fight.
1. Cemetery of Ash, Dark Souls III
Once Iudex Gundyr is defeated head to Firelink Shrine, light the bonfire, and explore the Shrine and the general area outside it. Perform the "tree jump" as shown in the above video to access an area that contains various upgrade materials. The important items are an Estus Shard and the Covetous Silver Serpent Ring+0. The Estus Shard allows you to upgrade your Estus Flask, giving you another use of the Flask. Talk to Andre to upgrade your Estus Flask. The Silver Serpent Ring+0 allows you to absorb 10% more souls from a defeated enemy. Grab the ring and equip it immediately. Use the souls you have to level up Vigor and Endurance. Exhaust Hawkwood's dialogue.
If you want an extra 1 or 2 levels before branching out of the tutorial area, farm enemies at Cemetery of Ash.