They're randomly found in containers around the world. The purple ones (Daedric, Primal, Barbaric, Ancient Elf) are only found in vet zones (2 of them are found in Cadwell's Silver zones, and 2 are found in Cadwell's Gold zones, but I don't remember which is found in which set of zones), so depending on your level it may be a long time before you find them.

Pages of the Dwemer motif (unlike the other motifs, the Dwemer one is split up into individual pages for each type of piece that you can craft - legs, chest, etc) are found in containers in Dwemer delves, and can be found at any level.

Just to follow up on the two previous posts and add some clarification:

1) Primal and Barbaric drop in the Vet1-5 zones (or Cadwell's Silver). Ancient Elf and Daedric drop in the Vet6-10 ones (or Cadwell's Gold). I've confirmed this on console, as I looted an Ancient Elf motif in Khenarthi's Roost (which is Cadwell's Gold for me) on XB.

2) Imperial drops at any level, so can be found in any zone, but is extremely rare. I just found my first Imperial Motif a couple days ago on XB (I'd been playing on PC since Early Access and did a LOT of farming prior to the Justice System).

3) You want to keep in mind that any purple motif you find in the world will require you to be of a certain level in one of the equipment skills. For example, you will need to be Level 6 in the materials passive (the one that allows you to craft higher level gear) in either Blacksmithing, Woodworking, or Clothing before you can read/use the Barbaric or Primal motif (I'm not sure which one) and level 7 for the other (either Primal or Barbaric). For Ancient Elf, you will need level 8 and Daedric, level 9. Again, this is only needed in one of the three equipment crafting skills, and requires you to spend skill points.

4) To read any of the Dwemer pages, you will also need to be level 9 in one of the crafts (again, this is the level of the passive skill that allows you to craft higher gear, not the level of the crafting skill itself (which goes up to 50)).

5) The Imperial style, however, does not require you to be any particular level, so can be learned as soon as you find it. The same is true, of course, for all blue motifs.

6) If you really want to get the purple motifs now, and have the money to purchase them in the Crown store, the advantages to you are not having to wait until veteran levels to loot them and not having to be a particular level in order to read them - you can use them right away. The disadvantage to doing this, however, is that you won't find any of the style stones needed for these motifs until you hit the veteran levels, or manage to get a few from deconstruction or hirelings.

7) I should mention that you can also check the guild stores for these motifs, if you don't have the cash, but have the in-game gold. You can also look for the style stones needed to craft them as well.

Guild traders seem to have them, but they overcharge, usually 7-20k gold. I did find an Argonian one for only 510

The blue motifs are selling on PC for around 300-400g right now. Anyone asking for more on console servers is out to take advantage of beginners.
If you are consistent in checking all containers, you will find all the motifs eventually, with the possible exception of Imperial. I bought a few of the purples when I was impatient, but I've found multiple copies of each since then. The only real advantage to knowing more motifs is the ability to use many of the style stones you find along the way, plus a few achievements. Crafting is so easy in this game, most players have one or more crafters, and there is no real market for crafted equipment. In short, your gold is better spent on increasing inventory (a must have for crafters) than motifs. If you keep looking you will find them. The information about researching traits is spot on...takes almost a year to learn all traits even with passives. While saving style stones is a money saver in the early going (15g ea from vendors), they are a pain as you advance since they use valuable inventory. Currently, I only keep two of the blues, in addition to the purple motif styles.

I've found most of them just grinding and the Imperial one in a quest...it selling for sooo much in crown store ;-;