Labeling something a shrine, does not mean you can't sacrifice at these spots in your home; every Hene Kai Nea and Noumenia, I offer libations of mixed wine and incense at my shrine to Apollon, Hermes and Hekate, every Noumenia, I offer mixed wine and incense to Zeus Kthesios at His shrine in my kitchen, and ever Agathós Daímōn, I make a libation of unmixed wine at His shrine. As explained previously, I don't have an outdoor altar; I have one indoors, and it also houses my continual flame to Hestia. It's at this shrine I do the bulk of my worship--it's my hearth. It has my offering bowl, and is very deity-neutral, just to make sure everyone I give sacrifice to might feel at home at it. It's located in my bedroom shrine--the actual space, decorated and kept clean for the Theoi.
My altar is not the altar the ancient Hellenes would have used. For one, it's not outside--something I'm grateful for as it's snowing outside at the moment--and for another, it's not made of stone. I don't make a fire on top of it--a good thing, seeing as it's made of wood--but have to use a bowl to do so. In ancient Hellas, an altar was called a 'bômos' (βωμός)--properly signifying any elevation--with an 'epipuron' (ἐπίπυρον)--a movable pan or brazier--used on top of the bômos so it could serve as an altar for burnt-offerings. The household hearth was used to make sacrifices as well, and thus served as an altar of sorts. It was named after the Theia of the home and hearth: 'hestía' (ἑστία). Some state-owned altars--especially when they were simply large fires--were named 'hestía' as well.
Lets look at these altars in a bit more detail; first the bômos.
In ancient Hellas, and always in sudden emergencies, altars were made of earth, turf, or stones collected on the spot. In the Archaic and Classical periods (600–323 BC) most altars were made of stone, either monoliths or built of cut blocks, thus was usually the case for stationary altars built at temples. The sides were sometimes decorated--and if they were decorated, the decoration was usually pretty impressive--but the altars were usually plain, apart from an inscription naming the deity the altar was dedicated to.
Most bômoi were isolated cubes, around one meter (three feet) high, but there were altars which were far larger. When I went to Germany, I visited the Pergamon museum and got to see the second century BC altar they house there for myself. Its foundation is approximately 36 by 34 meters (118 by 112 feet) at the base, more than 6 meters (20 feet) high, and decorated with an elaborate frieze, about 120 meters (394 feet) long, showing the Titanomancy. The upper area, accessed by a wide staircase, was framed by a colonnade and here the actual sacrificial installation was placed. Needless to say, this type of huge altar was most often exception than rule.
The sacrificial altars were either square or round, sometimes with an indentation on the top for a fire, or sometimes with a hole, leading down to an eschára. An altar for libations or blood sacrifice could have a drain for the liquid. The indentation--or even the hole--could be used to steady an epipuron. The materials used were often limestone or marble, stones not very resistant to heat, and thus, an epipuron was used to protect the bômos below. Even with that, the sacrifices would render the altars black from soot on the top and spotted by the blood on the front, and from time to time they had to be touched up with stucco or lime.
The epipuron was usually a brazier, often with either one or three feet, and made of precious metals which could withstand the heat of a fire or the coals used to burn incense. In household worship, epipuron seem to have been used as altars, without the bômos to put it on. This meant that these portable altars made of metal, stone, or terracotta were used in household worship instead of, or in conjunction with, the hearth of a house; hestía. Whether these domestic altars were used for full-scale animal sacrifice is uncertain and the offerings made here were probably cakes (especially at Noumenia), incense, libations, and perhaps cooked food. In houses where there was no fireplace, an epipuron could serve as a heat source.
The altars themselves were used to burn the meat from animal sacrifices, incense, or bloodless offerings like cakes, fruits and breads. Pieces of meat were sometimes placed on top of a fireless altar as a gift for the Theoi, and were taken by the priests or priestesses later that day for their own consumption or to burry. On some altars, blood sacrifice was forbidden; the bômos of Apollon Genetôr ( 'the Begetter') at Delos, for example. In all cases, the sacredness of the altar was fundamental. Anyone seeking refuge at an altar was promised protection of the Theos that altar and shrine were dedicated to. To take a fugitive from the altar by force was sure to cause the wrath of the Theoi on those who took him or her. Killing a person near an altar caused severe miasma and would lead to purification rites. Most likely, the altar would be out of commission for a period of time.
As said, altars were located in front of the temple, not inside it. If a temple did have an indoor altar, it was almost always used for bloodless sacrifices. The bômos almost always faced east, in front of the temple. If a temple was replaced by another, the altar usually remained in place. In some cases, this led to a misalignment of temple and altar. The altar of Athena Polias and the Erechtheum on the Athenian Acropolis is a great example of this. It was doubtful this was seen as a huge problem, though.
Bothroi--offering pits--were usually dug when the occasion called for it, and closed up afterwards. It seems that in some instances an epipuron was also an acceptable altar for the Khthonic Theoi. As written previously, the Khthonic Theoi received special nighttime offerings of black animals, unmixed wine and special libations of milk and honey. Animal sacrifice was always done in a holókaustos--a sacrifice where the entire animal was burned and none of the meat was saved for human consumptions. It makes sense this type of sacrifice was done in an enclosed space; the temperature would have gotten high enough to burn most (if not all) of the animal.
Another term for a Hellenic altar one might find is 'thusiastérion' (θυσιαστήριον). It is used mostly in context to later, Christian, texts where the thusiastérion described illicit pagan altars to the Theoi, as offset by the 'proper' altars to God. Needless to say, I won't be using it much, simply because the ancient Hellenes did not.
The above list is non-exhaustive, but gives a decent overview of the terms and types of altars used by the ancient Hellenes. There was, of course, variation in actual practice, and a good few altars broke this mold. For modern Hellenists, it's a good starting point for the construction of an (outdoor) bômos.