Ud 
There are a number of different types of sign in Sumerian - they used logograms (a symbol that represents a word) and syllabic signs (a symbol that generally represented a consonant, followed by a vowel, followed by a consonant, although there were symbols that represented a vowel-consonant pair or a consonant-vowel pair).
This is where things get fun. We really don't know what the vowels were, they were never written down in any of the early Middle Eastern languages. Most of the vowel values are based on what other people - such as the Greeks - thought they heard. The bilingual and trilingual texts that exist have phonetic approximations, usually of names as these didn't have an exact translation.
Here are some attempts to render the sound of Sumerian, to give an idea of how scholars think it worked.
First few lines of Gilgamish
Conversational Sumerian
It's much, much easier to find Akkadian and Babylonian speech, as Semitic languages follow similar rules. It's therefore easier to reconstruct. Besides, the Babylonians are better-known. However, this makes it rather boring. Anyone can do the possible, given long enough.