The Sumerians kept altars (guhšu 𒈞𒋙) to their personal gods in their homes as a place for offerings and rituals. Reconstructionist Sumerian pagans should endeavour to do the same. However, it is important to understand two significant points before constructing a Sumerian altar:
Firstly, the Sumerians held their altars to be physical dwelling places of the gods. The Sumerian words for "house" and "temple" are the same, e 𒂍, because the first Sumerian temples were houses that were built for and dedicated to a deity. This implies not only asking a god to come into your home, but offering a space to them to dwell in; this space will now belong to the deity, and you accordingly should act like a guest in that space.
A Sumerian altar will always include some kind of image of a god; this image is to be treated as though it holds the spirit of the god themselves.
Therefore, if it is not desirable for any reason to invite a deity into your home, you should not set up a Sumerian altar.
Secondly, that the Sumerians believed that the material and spiritual worlds reflected each other. This means that physical items placed on a physical altar have an exact equivalent in the spiritual world.
An altar space, being a literal home for that deity, is to be kept in appropriate conditions. In particular, the Sumerian deities require that any person entering the altar space be clean, and that their dwelling be kept similarly clean.
Remember also that the energy around an altar reflects the energy in the dwelling place of that deity; it is important to maintain a pure, clean energy in the altar space.
If you consider that it would be too much effort to maintain a home for a deity, with proper cleanliness (physically and spiritually) in the space around it, you should not set up a Sumerian altar.
If you find after setting up an altar that you do not have the energy (including mentally) to maintain it, you should dismantle it. Do not strain yourself attempting to maintain an altar; better to dismantle it than allow it to fall into disrepair.
The most important thing on a Sumerian altar is an image of a deity. This should ideally be a statue or figurine if at all possible, but if one isn't available, a printed image or even an appropriate cuneiform sign will suffice, as the Sumerians believed the cuneiform signs to hold the essence of the thing they represented. Choose the image carefully, because it will contain the very real presence of the deity. If you use a statue, it should be cleaned as it's being dedicated, and regularly after that (wipe it with fresh, clean water, particularly the mouth). This image should rest upon an elevated platform, which serves as a dais (Sumerian: barag 𒁈).
A Sumerian altar should also include a votive statue. This is a second statue or figurine, representing the worshipper, which should be placed in a position opposite to and below that of the divine image, in a stance of worship. The votive statue represents the worshipper, constantly praising and glorifying the gods.
Incense is important when praying, making offerings, or performing rituals at an altar. The Sumerians believed incense to be the medium which carried words and prayers to the gods, while at the same time purifying the space of the altar and filling it with an odour that is pleasing to the gods. Any type of incense is fine; incense sticks and loose incense are both acceptable.
Candles do not play nearly as major a role in Sumerian ritual as in later, Western-influenced pagan thought, but it is useful to place some on the altar and light them during ritual. In a Sumerian temple, the altar would be located in a dark inner sanctum, and candles therefore fill the space with light for the deity.
Live plants, which were seen as pleasing to the gods, can also be placed on an altar, adding colour and vibrance. Gold and silver items are valued; those of lapis lazuli even more so, with lapis lazuli being particularly sacred to Inana. A bowl of water demonstrates ritual purity. Further items can be placed according to the domains of the gods, such as a reed stylus for Nisaba, or a clay bowl of earth for Ninhursaĝ. Creativity and expression are encouraged here.
An altar can include further votive figures, beyond the worshipper; figures of temple personnel such as scribes, or even animals. Don't be tempted to make the altar too cluttered, though; an ideal altar should not be too busy that it's hard to make out what's going on.
Priests in Sumer may ceremonially have approached the altar naked, on occasion, to demonstrate humility and subservience before the gods. This is not a requirement, but it is required that the altar be approached in a suitably humble and reverent fashion.
The great temples of Mesopotamia (ziggurats) were at the top of long, winding staircases, in order to not approach the gods directly. It is not necessary to place an altar in a difficult-to-access position today, although it certainly may help to promote humility; the main thing with which the gods are concerned is that proper respect is maintained by worshippers.
An altar should further contain those items which are used in particular rituals, divinatory materials, or additional necessities for specific practice. Again, though, an altar should be free of clutter; seasonal items, or those for particular rituals, can be stored when not in use.