Refer to gathering in The Elder Scrolls Online, what you may come to your mind first? Well, as for me, gathering is the most simple but crazy thing ever. In one word, you just click to win. No pre - requisits skill is needed to level up. Every players can loot everything, not a big deal really. The only issue is that some resources are phased for you and some are not.
To gather, find a resource and press E or whatever your default interact button is.
Crafting weapons and armor and other things can make you very powerful and crafting is very open to everyone, you don't need a lot to level your skills and some of the weapons you can make are very overpowered for your level (also tradable). A level one Superior Greatsword is 23 damage, using items you can get off an NPC (Dwarven Oil).
Resources are either phased to your character (only for you) or they're free for everyone. Since ESO uses megaservers, everyone is a pretty broad term, but generally speaking everyone that can see that specific node can loot that specific node, from my understanding.
One of the important reasons for this is because if nodes are made private, everyone can farm a node, inflating the economy with resources. ESO doesn't have much of a trade / barter economy, but it still helps to restrict the supply and make players fight over resources, to some extent.
Books are a unique resource in that reading one will provide you with a possible skill up in the relevant category that the box belongs to. So you'll randomly come across the book and read it and gain Blacksmithing for instance. This isn't for every book, but the good thing is that books read are unique to you.
As far as I'm to understand, crates and sacks and other containers in the world are also phased and will randomly respawn after being looted. These contain primarily crafting recipes and materials.
Not - Phased Resources
Resource Nodes, Locked Chests
Resource nodes aren't phased and someone else can gank them from you without any issue. Locked chests are also first come first serve. There are five effective resource nodes (and a lot of random "nodes" like Torchbugs and various other kinds of misc items and bait). Wood (for Woodworking), metal (for Blacksmithing), runes (for Enchanting), reagents (for Alchemy), and leather / cloth (for Clothing). These items are found scattered throughout the world.
Non - phased resources are free - for - all.
For wood, metal, runes, and cloth you can can get the Keen Eyes skill which will make the nodes glow when in range to make it easier to find them. It's definitely worth the extra skill points if you want to gather a lot.
To find resources, you pretty much have to wander around and loot them on the ground. They are free for all, outside of containers and regular chests, so you're going to have to be vigilant. Additionally, phasing plays a huge role in what resources you can and can't gather. For instance, in some phases there are no enemies in the area and the area is peaceful (generally after the end of a quest line) or you gain allied status with the enemies (a great example is ghosts) making the area peaceful to gather in. Some phases are full of enemies (usually pre or mid - quest).
Resources are located in level appropriate zones, so if you want to craft a specific level item, those resources are in that equivalent leveled area. You'll see Iron in the newbie areas, for instance, and Steel the next map up.