If you have a single bird, or birds that don't get along and don't preen each other, it is up to you to preen these areas. Luckily we as humans can usually get away with gently scratching the bird's head and neck, and gently removing any pieces of food or dirt we find. What to do if a blood feather breaks The keratin sheath surrounding a blood feather acts like a straw when broken, and blood flows through the straw with little resistance. It is very difficult to stop a bleeding blood feather from bleeding. Birds are very small creatures and it doesn't take much blood loss for them to bleed to death.
Most people recommend needlenose pliers or something called a hemostat.
After removing the feather, the follicle will bleed, and you can staunch the bleeding with corn starch or flour. Note carefully Cathy's warning about styptic powder. The ones from the hardware store have different ingredients, some of which are carcinogenic. I used to use hardware-store cyanoacrylate adhesive to seal my own fingers when I got bitten, until I found out the difference. Surgical adhesives are specifically meant to be used on living tissue, and have no such carcinogenic compounds.