Blood flow, the vessel wall and the constituents of the blood do not act in independent groups. Instead, the formation of a blood clot requires all three to be involved and to interact with each other (with the exception of very small breaches which can sometimes be patched just by platelets without the aid of the coagulation cascade).
Damage to a blood vessel is the first event in the generation of a blood clot. Blood that flows through a breach in the wall of a blood vessel will be exposed to subendothelial tissue and to tissue factor, the latter being particularly important in beginning clotting. The damage can shear off endothelial cells from the wall of the blood vessel around the hole, also resulting in the blood coming into contact with tissue factor and other subendothelial proteins.
The breach and the disruption to the endothelium produce turbulent blood flow and this is detected by the platelets and acts as a further stimulus to clotting.
Once the damage has occurred the surviving endothelial cells do not simply sit around passively bewailing their lot and waiting helplessly to be rescued like damsels in distress. Instead they refuse to take things lying down and switch from being mild mannered co-operative cells that facilitate smooth, uninterrupted blood flow into an active anti-haemorrhage vigilante taskforce. The angered endothelial cells secrete vasoconstrictor substances that cause the smooth muscle of the wall of the blood vessel to contract, thus reducing blood flow. In case factor VII has not apprehended the gravity of the situation, the endothelial cells express tissue factor themselves to ram the message home. The platelets also experience the wrath of the endothelial cells: von Willebrand factor is expressed on the surface of the injured endothelial cells and orders the platelets to shift their butts and stick themselves somewhere useful.
The platelets themselves are already moving into gear even without the exhortations of the endothelial cells. Their Gp1a receptor allows them to recognise exposed collagen and bind to it. This directs platelets to the site of the damage. The Gp1b-GpV-GpIX complex permits platelets to bind to von Willebrand factor. The GpIIa/IIIb receptor locks onto fibrin. Binding at each of these receptors also activates the platelet and causes it to release it granules, the contents of which include extra clotting factors to bring more ammunition to the battle.
Damage to the blood vessel reveals tissue factor to the blood. This activates factor VII. The activated factor VII stimulates factor X which in turn tells factor II that all is not well. The rousal of prothrombin from its dormant state into thrombin is the trigger that is needed to convert fibrinogen into fibrin. Thrombin converts factor XIII into its active form and the fibrin molecules cross link to provide a dense scaffold that traps erythrocytes and provides another binding site for platelets (via their receptor for fibrin).
Thrombin feeds back into other parts of the coagulation cascade to drive it on, particularly the intrinsic pathway.
Superimposed on all of these interactions is the possibility for intercession by the inflammatory system. Both platelets and endothelial cells can be stimulated by inflammatory mediators, a phenomenon that can be useful because those events which demand an inflammatory response will often require activity from the clotting system.