If and when we desire to eat meat (other than the sacred meat of korbanot), we may do so anywhere we choose, but we must properly slaughter the animals we eat first.
In the pasuk commanding Sh'chita, G-d says "(slaughter the animal) as I have commanded you". Yet we do not find the details of Sh'chita in the Written Torah. This pasuk is one of the sources for the concept that the Torah consists of a written portion and an Oral Law – both the word of G-d.
Non-sacred meat does not have the same restrictions as sacred meat (i.e. ritual impurity – yours or the animal's – is not an impediment). Many other halakhot, of course, do apply.
An animal must be killed before its meat is taken. This is the universal prohibition (it is both one of the 613 and one of the 7 Noahide Laws) of "Limb from a living animal". Blood must be removed from meat before we may eat it.
Listen to Torah Tidbits Audio For Parashat R'ei: