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There aren't any books on the market about authentic Sumerian magic right now that aren't academic in their approach. This is because Sumerian magical practices are only attested on a small amount of cuneiform tablets—56 tablets, totaling approximately 62 magical operations, as of 2016—leaving us with an incredibly small sample size to draw our conclusions from.
We have a much larger sample size for Babylonian magic, including series of multiple tablets, like the Utukkū Lemnūtu, or the much-copied Maqlû ceremony, not to mention the various prognostication manuals. However, Babylonian magic was practiced in Mesopotamia after the Sumerians ceased to exist as an ethnic population, so confusing the two for each other would be an amateur's mistake.
What we do know about Sumerian magic is that it was primarily apotropaic in nature, often involved the recitation of a legend explaining the origin of the malady to be remedied, and functioned on "theistic operative force," i.e., invoking a deity as the ultimate source of the magic used to treat the problem, and identifying the human as an agent working on their behalf.
For example, the following is a translation of "Incantation F" from the tablet MS 4549/1:
It is an incantation. Asarre (was out walking). A big snake was slithering along. The big snake produced venom. To his father, Enki, Asarre sent a messenger. (Enki answered the messenger:) "What does he not know? What can I teach him? Pour out water from the Tigris River, water from the Euphrates river, and give it to the bitten person to drink. The thing of its own accord will run away!"
This incantation invokes the god Asalluḫe under his abbreviated name, Asarre, through the recitation of a legend during which he first learns to treat a victim of snakebite. Not only does the magician empower his own actions by recalling this legend, but he amplifies this power by including what Assyriologists call a "magical formula," a phrase found throughout the corpus that was intended to produce a magical effect.
In the example above the magical formula is: "What does he not know? What can I teach him?" This establishes that not only is Asarre empowering the magic, but that Asarre's father, Enki, is the ultimate source of this power. Since Enki is one of Sumer's highest ranking deities, his authority over magic is incontestable, thus making any spell or magical action that he created permanently effective.
Thus, by recalling the legend of Asalluḫe, the magician "becomes" him and uses the divine authority of Enki to make his (the magician's) current treatment against snakebites as effective as the legendary one.
Other examples from this time period (ca. 2600–2340 B.C.E.) feature incantations against scorpion sting, sickness, misfortune during construction, and possibly ghosts (or other nuisances) "from the Netherworld" who can afflict humans.
Despite its appearance in the quoted incantation above, the magical formula "What does he not know? What can I teach him?" is actually rarely attested in Sumerian magic. It becomes much more common in Babylonian magic, where the god Marduk replaces Asalluḫe as the focus of the legend, and Ea replaces Enki as the ultimate source of the magical act.
The most common magical formula in Sumerian magic is: KA+UD du₁₁-ga DN, "It is the incantation of deity-X!" In Babylonian magic this becomes: šiptum ul yattun šipat DN, "The incantation is not mine, it is the incantation of deity-X!" This formula serves as the closing line for 34 of the 62 known examples of Sumerian incantations, with the goddess Ningirima functioning as creator of the incantation in 27 of those examples.
So, if you're interested in performing authentic Sumerian magic, then you'll want to:
Familiarize yourself with Sumerian storytelling so that you can create a believable legend about whatever issue you're seeking to effect through your magic.
Insert the goddess Ningirima into this legend as the agent who discovers the first occurrence of the problem in documented history.
Have Ningirima devise a remedy for the situation based on whatever medical or magical approach you think will work.
Optionally: have Ningirima consult with her superior for advice regarding the situation. Where Asalluḫe or Marduk go to their father, Enki or Ea, Ningirima is documented in Sumerian magical literature as consulting with the god Enlil.
Perform this remedy using one of the magical formulae, most likely "It is not my [magical act], it is the [magical act] of Ningirima!" source!