A ritual offering is one that is presented to a deity in a formal act of devotion. For the purpose of the modern day Sumerian reconstructionist, this would generally take place at an altar dedicated to their personal god; for more details on setting up an altar, see here.
An offering can be made at any time and, as discussed elsewhere on this site, does not need to be done in a ritual; the act of ritual dedication, however, is a deeply personal link between a person and a deity. It shows that the worshipper genuinely values the gifts that have been given to them by the gods.
The most common offerings made to the gods are those of food and drink, a meal offering called gizbun 𒆠𒁉𒃻. When given at an altar, these offerings are believed to nourish the gods. The best offerings are therefore natural and nutritious foodstuffs; meat and poultry, fish, bread and grains, fruits and vegetables. Avoid offering junk food, and that which is overly processed.
Water and milk are excellent offerings, as these are intimately connected with the nourishment of life; wine and beer are also considered good offerings. Again, processed and sugary beverages should not be given as offerings.
There is no prescribed formula for making offerings. The Sumerian tradition is much less concerned with orthodox recitations than many other faiths. It's not required to say particular things in exactly the right order, but it is required that ritual forms show devotion and sincerity. Be expressive; language is a gift of the gods and we are encouraged to make use of it. However, outlined below is a general idea of what a ritual offering to a Sumerian deity might look like.
1. Prepare the space for the deity. What this may look like is down to your own conception; you may wish to purify your altar space before you begin. You should be clean before approaching the altar. Once your altar space is cleansed or purified to your own satisfaction, light incense and candles.
2. Praise the deity. Express your thanks for the deity's blessings. As ever, praise should be genuinely given - you shouldn't feel like you're reciting a list. Keep it sincere and heartfelt.
3. Politely invite the deity to come into your space. As in many pagan traditions, Sumerian gods will generally give a sign - openly or personally - to show that they have accepted your invitation.
4. Make your offering to the deity. Allow sufficient time for the meal to be consumed; a few minutes should suffice. The deity, of course, does not physically consume the meal - the Sumerians believed that the offerings nourished the gods on the spiritual plane.
5. Thank the deity for their presence in your space. Prayer and petitions may be offered at this time.
Unlike some other pagan traditions, there is no need to formally 'close' the connection; the deity will depart at their own leisure. You can now extinguish the candles.
Standard practice in Sumer was that you could and should eat the offerings afterwards; particularly large offerings would be distributed amongst the poor. Liquid offerings should never be consumed, and should be poured out (this is called a libation) - ideally onto the ground, but if this is not possible, a clean sink will suffice.
Food and drink are the most common things offered to a deity, but they are far from the only offerings you can make. Artistic offerings are very much appreciated. The arts were particularly valued in Sumer, and offerings in the form of paintings, sculptures, or praise poetry would be highly regarded.
It is also possible to dedicate a home, temple, or dwelling to a deity, using similar rituals. Be aware that if you are consecrating a space to a particular deity, you become responsible for the upkeep of that space for the purpose for which it was dedicated.
Offerings of precious stones and metals are valued. These items can remain on the altar or can be put to other uses, but of course a consecrated item should always be handled with care. Gold and silver are especially valuable, lapis lazuli even more so, as this was the sacred mineral of the gods in Sumerian culture. Inana in particular is associated with lapis lazuli.
Finally, it is possible to dedicate work and effort to the gods, particularly that done in their service or upholding their order.