Blood is the preferred fluid of Armok, as well as the fluid that most living creatures contain within their bodies. Some creatures will have ichor instead. It is unfortunate that losing this fluid tends to be invariably fatal to those who possess it.
Blood tends to spread everywhere; you will just have to get used to it. Or go insane, your choice. It is possible to remove blood from a soil floor by building a dirt road on it. Allocating bloody indoor underground areas as a meeting area seems to increase their cleaning priority and they will get cleaned pretty quickly if you have enough idle workers. However, this does not seem to work for above ground areas and have in fact the opposite effects. It is better to forbid an area with blood in above areas as rain will randomly clear tiles where it touches it. To rid of blood splattering on a rough wall, designating the splattered area to be smoothed will make it disappear.
Dwarf walking on tiles with blood (smear) will spread it to the next tile, where it will form a spattering of blood, then a smear. That is why blood areas tends to grow quickly on above ground when heavy traffic is there. A setting in d_init.txt permits disabling the spreading of blood.
Brooks and similar sources of water appear to replicate any blood that falls on their tiles, resulting in an endlessly growing carpet of blood. This can be dealt with by covering the offending brook tiles with walls or floors.
 Assorted Blood Types
 Bloodless Creatures
Some creatures, when injured, may leave residue like a normal creature would bleed, but not actual blood. For example, a Titan made out of salt may leave piles of salt where it was injured.
 Collecting Blood
Beyond the obvious method of injuring creatures, barrels full of blood can be brought with a dwarven expedition upon embark, and bought from dwarven and human civilizations in trade. The use for this is uncertain, though the stuff may appease Armok until you can start "producing" it on your own.
 Disposing of Blood
Selecting blood inside a barrel for dumping does not empty the barrel. Using the workaround for dumping liquids from lye buckets works - view the contents of the barrel, select the blood and forbid or dump it. Alternatively, forbid/dump the blood from the stocks screen in 'liquids'. Then order the barrel to be brought for trading at the depot.