The process of arresting bleeding is called Haemostasis. The agent which helps in this process is a Haemostat.Haemostasis comprises of  4 events 

Vasoconstriction
When bleeding occurs due to damaged blood vessel, platelets present in blood come together to the site of injury. They become sticky and release "SEROTONIN", which constricts (narrows) the blood vessel, thereby reducing blood flow.

Platelet Plug formation
Platelets attract themselves at the damaged site. They release many substances mainly ADP (Adenosine Diphosphate) and this quickly attracts more platelets to this site. This accumulation of platelets quickly forms a temporary seal called 'platelet plug'. Thus, blood loss through vascular opening is stopped.

Coagulation
It is a complex process which involves many factors. It is described in a simplified manner as given below: -
Thromboplastin is liberated from the damaged tissues and damaged platelets. This converts inactive Prothrombin, in the presence of Ca ions (Ca++) into active thrombin.Thrombin converts soluble fibronogen in the presence of Ca++ into insoluble fibrin.These are protein fibres that form a mesh where blood cells get  entrapped and thus form a blood clot.    

Clot Dissolution 
Once the blood clot is formed, clot retraction starts. Plasminogen present in  blood is activated to form plasmin which brings about lysis of fibrin clot thereby causing clot dissolution.