When an injury occurs in a blood vessel, here are the steps we go through.
Platelets and Fibrin are the important things that we actually get as products of coagulation that seal up a wound. But the activation of them is a complicated process. Which is a good thing for your body! If it were an easy reaction, we could get our blood spontaneously clotting on us and that would be BAD.
Here's another way to visualize this:
In first forming the platelet plug, it's important to note that it's the exposed collagen fibers that are attracting platelets. The normal, healthy state of things is to NOT have platelets sticking to blood vessels. The ability to not stick is ensured by the blood vessel lining cells (endothelial) releasing prostacyclin to prevent platelet sticking. But with damage, that isn't released and instead collagen causes platelets to stick. This can be visualized here:
Now for the actual clotting part after the platelet plug, for now I have some videos. If you want to cut right to the chase and a great explanation, watch the last video.
Here's a not fabulous animation but an animation nontheless...
This short clip I just found helpful to visualizing how the different factors work together to activate factor X then prothrombin, to activate thrombin which they refer to as the "thrombin burst" because it creates a large amount then creates a positive feedback loop to further increase the effect.
This is the best video I found! I like how concise and understandable he makes it, looking at the big picture and working backward from there. Hope it's helpful for you too.
All clotting factors are made by the liver, except 8 and PAF3. (Platelet activating factor is made by white blood cells.)