I do favor prevention by placing a small amount product containing glycerin onto the nose. This physically protects the nose lining from being dried out and then torn open. Products readily available in pharmacies include Ayr Saline Nasal Gel, ENTsol Nasal Gel, K-Y jelly, NasoGel, and Rhinaris Gel.
Once the nose bleed has started, the first step is to not panic. First aid like with any wound, can help. Direct pressure by gently squeezing the nose is helpful. Also, slightly tilting the head backwards and lying motionless can help. Applying ice to the back of the neck causes the blood vessels in the head to constrict because of the cold and in theory the blood vessels in the nose could constrict too, thus slowing the blood loss. Try not to blow your nose, even though the scab often plugs up the nose, reducing or preventing breathing through the nose, which is admittedly uncomfortable. If the scab comes off, the bleeding may resume. Over-The-Counter products are available: D-Stat Dry, QR powder, and XS Powder, are the ones I have found. In a 2008 study by Wang et al, these 3 products were compared for their ability to stop bleeding following 4 types of radiologic procedures, not nose bleeds. The results favored the QR Powder > XS Powder > D-Stat Dry. When physicians are consulted for severe or recurrent nose bleeds, technically called epistaxis, they may cauterize the issue. In essence this means to burn and scar the tissue to stop and prevent further nose bleeds. Silver nitrate on Q-tips or a metal probe with electrical current can be used to cauterize the nose mucosa.
Once you or a loved one has had a severe or recurrent nose bleed, please do not forget about trying to prevent them. I have had a lot of experience with this, because of two circumstances. First, my son has recurrent nose bleeds at the drop of a hat, before my very eyes, doing nothing but sitting there. Second, I went with my son and the local Boy Scout Council, Blue Ridge, to Philmont Ranch in June of 2009. We were in northwestern New Mexico, elevation 6,000 to 12,000 feet elevation, usually about 9,000 to 10,000 feet, going backpacking. Out of our contingent of 10, 6 had nose bleeds and 3 had recurrent, nearly daily nose bleeds, sometimes multiple per day. Our experience was the norm. It's DRY up there.
Disclaimer: I do not own stock in any of the companies whose products I have mentioned above nor have I been paid to mention them (although I am very open to the idea, since I have 2 kids in college.)