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Motifs come in the form of books. So the "orc motif" is a book that you can read - after that you can craft in the orc style.
At the start, you can craft in your own race's style. Then you need to find/buy and then read the other race's motifs before you can craft their style.
The motifs can be found by searching containers, dressers, nightstands etc. or bought from guild traders. Some are rarer than others, and some you won't find naturally until you reach the higher zones.
To craft an item in a particular style you need a style material (e.g. a moonstone for Khajit style). These also drop naturally from containers etc. or you can buy the common ones from the blacksmith. (Or buy them from guild traders). The rarer motifs also have rarer style materials which aren't always so simple to obtain.
For completing writs, the style of the crafted item is irrelevant.
A trait stone is a second material you can use up OPTIONALLY during the crafting process to imbue the items with a particular quality (i.e. trait). So an "almandine" gives the item the property "well-fitted", which means wearing that item lets you use up less stamina when sprinting.
Before you can apply a trait stone, though, you need to have researched the trait for the item in question. That means finding an item that already has that trait, then "researching" it at the crafting station (the far right icon at the crafting station lets you do this). Once the research process is finished, you have permanently learnt that trait for that item. The process takes time. The first few traits you research take a few hours/days to learn, but there are nine traits and when you're learning the ninth trait for an item it can take up to a month for the research process to finish.
For writs, you do not need to apply a trait to the items.
There are special crafting stations out in the wild that will let you make items that are part of sets with special bonuses. But these sets require you to have learned a minimum number of traits on an item before you can craft it in the set version.
Google "ESO crafting guide" and there are many online resources that have more in-depth info than this simplified overview.