In surgery, blood is always an issue. If a blood vessel is punctured and blood spurts out, they will electrocauterize it which seals the vessel. This is the fastest and most effective method. Another way is to tie the vessel shut with a suture. There are always cloth gauzes to sop up blood. You can also temporarily clamp the vessel with a hemostat (aka snap) clamp instrument. Another option is to decrease the flow of the blood, either by injecting epinephrine. Another option is to use hemostatic agents/powders/gels which glues up the area. Sometimes we use the tourniquet to restrict the flow of blood to limbs.

In rare cases - like in a liver laceration - surgeons place gauze in the laceration to have an hemostatic effect (liver packing). After some time the gauze has to be removed (unless an absorbable material is used).

Forgotten gauzes inside a patient is a source that inflamation and potential site of infection.

A gauze bandage should be used on a sealed wounds because if it is put on a fresh wound that has pus and blood leaking, you need to change it before the secretions get dry and stuck as when you change the dressing, you will need to wet it with water to get it off or shower. If this is an incision that has been sutured (sewn uo or stapled) you can cover it with sterile guaze dressings but for most wounds occurring at home, guaze can stick with secretions and untreated Telfan dressings are better for larger than bandaid covering as Telfan doesn’t stick.

It really depends on your certification level and setting. An accomplished thoracic surgeon in a level 1 trauma center will be substantially different than a boy scout with EMS less than 10 minutes away.

For lay people (I assumed a thoracic surgeon or EMT would not ask), it's pretty simple:

Call for immediate advanced life support

Be prepared to assist breathing

Supply high flow oxygen if available (medical grade and with the appropriate device)

Treat for shock / prepare for CPR

Frequent monitoring of vital signs (< 5min)