I am not sure what you mean by "employ an ancient symbol(s)", but assyriologists use a couple of different standard sign lists for getting from cuneiform signs to a Latin alphabet equivalent. Keep in mind, however, that this is only one step; an additional step is necessary in order to translate the transliterated signs into English. Also, my own focus is on Akkadian (the language of the Assyrians and Babylonians), and not any of the other cuneiform languages, such as Sumerian, Elamite, Ugaritic, etc. The process of transliteration and translation is similar, however.

Anyways, most assyriologists use either R. Borger's Assyrisch-babylonische Zeichenliste (1981), or R. Labat's Manuel d'épigraphie akkadienne (1976). These books are essentially sign lists, which list all known cuneiform signs, and then lists their various values and interpretations.

When faced with a new Akkadian text (such as this drawing of the Cyrus Cylinder), they will use the aforementioned sign lists to transliterate the signs into pronounceable Akkadian words in a Latin alphabet. The result is what you would see here in the left column of this edition of the Cyrus Cylinder. Akkadian is a syllabic language, meaning that a single sign generally represents a single syllable. A string of cuneiform signs then can be read together as a word, and words are stringed together to compose sentences.

The process is complicated by a couple of major features of cuneiform: first, a sign can have multiple possible values. For instance, a single horizontal wedge can have the phonetic value of ash, as, rum, ru, dil, or til. Think of it as a very difficult sudoku puzzle. There a number of possibilities for each sign, but then each sign taken in context with the surrounding signs really can only correspond to select number of combinations to form an attested word.

Second, signs can also be logograms, meaning that an individual sign can be read as an entire word instead of with its phonetic value. In Akkadian, logograms are borrowed from Sumerian. That aforementioned sign also has a logographic value of ASH, which is Sumerian, and has a number of different Akkadian meanings, including aplu (son), ina (in), and shumma (if). Again, the way assyriologists figure out what value to assign to a single sign is based on the context of the sign. What combination of signs around it can be made into some sensible phrase or sentence?

Anyways, if you want to find the cuneiform symbols that can be strung together to mean words that in English mean water or slumber, your best bet would be to start with a simpler dictionary like the Concise Dictionary of Akkadian, edited by J. Black, A. George, and N. Postgate, and search around for the English words you want and their Akkadian equivalents. The entries will often also give you the logographic values as well.

So, for example, "water" in Akkadian is mû, which can be written in signs with the signs for "MU-U" or just "MU". Alternatively, the logogram for mû is the sign A. So, as you can see, there is no simple way to translate cuneiform into English. There are a variety of ways to say even a single syllable in Akkadian, and Akkadian grammar and style differ from period to period and genre to genre.

A final resource I will recommend is John Huehnergard's Grammar of Akkadian, which is by now the standard for any class taught in Akkadian. Check it out if you are interested in learning the grammatical structure of Akkadian, or the finer points of cuneiform signs.

First, you should probably get a good grammar and dictionary of the underlying languages so you don't produce unintelligible nonsense or at least make the english vorlage marginally less visible. The standard grammar for Akkadian is Huhenergard's A Grammar of Akkadian and of Hittite is Van Den Hout's The Elements of Hittite. These will also contain useful basic signlists. For signlists, the standard cuneiform signlist is Labat's Manuel d'Epigraphie Akkadienne, which is avaliable online for free at several places. It is admittedly in French, but it is reasonably trivial to understand the French glosses on the logograms. The Electronic Pennsylvania Sumerian Dictionary (http://psd.museum.upenn.edu/epsd/nepsd-frame.html) is an excellent reference for Sumerian words and phrases, although you will want to be careful about not attempting a bad back-translation. The Open Richly Annotated Cuneiform Corpus (http://oracc.museum.upenn.edu/projectlist.html) may also be helpful, particularly if you want to find a stock phrase to use(the translated texts are written out sign-by-sign in Roman characters and have mouseover glosses in English so you need only consult a signlist to see what the corresponding grapheme is).

Also, to save you some work, if you want to do something with water, gods, and slumber, you may want to write something relating to the Abzu, the subterranean watery domain of the god of wisdom Ea/Enki. Do you have an idea of what these symbols are for or what sort of thing you want to write?