I found several places in Torah where we are told not to eat the blood (Genesis 9:4; Leviticus 3:17; 7:26; 17:12, 14; 19:26; Deuteronomy 12:16, 23; 15:23). Since most of us do not slaughter our own animals for meat, we are left with the task of trying to get the blood out of the meat long after it's been killed, packaged, frozen, and driven to our local grocery store.
What to do? As is often the case when I have a question about how to run my kitchen, I turn to the Jewish people for help. I do make the attempt to get as much blood out of the meat by following the process outlined here. Keep in mind there is a process for fowl as well.
Today I am kashering a flat iron steak for tonight's erev Shabbat meal. I'm soaking the steak now and will do that for about an hour. Then I'll let it drain on a baking rack for a bit (in the sink) until it's just moist enough for kosher salt to stick. Then I'll cover it with a good bit of salt, not completely, because the blood has to drain out, but on all sides with enough salt to draw out the blood. I have a cutting board I use specifically for this process, slant it into the sink, and let the meat hang out there for another hour. Then it gets triple rinsed. At that point, the meat is ready for marinade or whatever I'm going to do to it (tonight I'm using this marinade).