It is advised that before you engage in a boss fight and start using consumables you try and learn as much about the battle as possible so you can make what you have count against your foe as buying these individual items from the merchant Vulgrim will increase in price.
Artifacts can be found throughout the world and they are required to upgrade enhancements. To complete the upgrade you will also need Essence of Chosen which are primarily obtained by defeating various Chosen enemies that are hidden throughout the map. The type of Artifacts you collect whether Angelic or Demonic will determine the enhancement you are able to get. You can view the crafting ingredients required for each enhancement upgrade by speaking with Ulthane.
Make sure you regularly return to the hub forge as the vendor there will randomly give you items that increase your power depending on how far you are in the story and also periodically upgrade your gear if you have the reagents. You will not be penalised in any way for returning to the hub forge and to return back to where you came from you just need to look for the circular rune icon on the teleportation menu.
The green bar in the top left corner of the screen is Fury's health meter and this can be replenished when it is low by consuming a Healing Shard or by using a Nephilim's Respite.
You will need to head out into the world and scavenge for a metal called Adamantine to upgrade your weaponry. Although there are certain crafting materials you can purchase from Vulgrim it is advised that you instead spend your souls on leveling up your attributes.
You may want to consider using Fury's Havoc form as an extra heal or save it for when you face a boss that you are confident of deafeating so you don't have to spend time working your meter back up or wasting an item to replenish it.
You will need to feed the souls you have collected to Vulgrim in order to gain the Atrribute Points need to level up your attributes. Attribute Points can be applied to one of three attributes: Health, Strength, or Arcane. Each attribute has it's own level scaling, which you can view in your Inventory.
Souls are automatically collected when Fury defeats enemies. Souls can also be obtained from breaking objects in the environment, as well as by shattering Lurcher Crystals. You can keep track of how many souls you have by looking in the lower right corner of the screen.
Enhacements can either be found through exploring or purchased from Vulgrim and they can be socketed into each of your weapons by Ulthane to provide additional benefits to Fury during combat. To receive the bonus effects from the enhancement you will have to wield the weapon that has the enhancement socketed to it.
Twister Elemental Wrath Attack:
An effective elemental wrath attack (mini-super) against stationary bosses or foes that are in groups is the twister from Fury's electric form. This attack stays in the battlefield for an extended period of time and can mix up enemies or stunlock them, allowing you to deal with the situation without feeling overwhelmed.
Remember that items other than your main potions have cooldowns. If you need to replenish a meter make sure you use the item before you enter the boss arena and wait for the cooldown to drop so it is fully replenished when you begin the battle.
To fast travel you need to speak to Vulgrim and select the Serpent Holes option from the list to view the available fast travel locations. Then just scroll through the different regions and fast travel locations to find the one you want to go to. Make sure you take advantage of fast travelling to visit Ulthane regularly so he can upgrade your weapons and enhacements.