DNA produces the RNA by a process known as transcription. DNA is a double-helix stranded molecule, so think of DNA as 2 vertical chains with different kinds of nitrogenous bases on them. These bases include Adenine, Thymine, Guanine, and Cytosine, but we will simply call them "A", "T", "G", and "C".
During transcription, the DNA unzips, so think of it that those two strands are now separated. The transcription occurs along ONE of these TWO separate strands. Once transcription begins, by the process of complementary basing, the RNA molecule is built. Where ever there is a "A" on that DNA strand, there will be a "U" (because RNA cannot consist of "T", the complementary of "A"), wherever there is a "C" on the DNA, there will be a "G" on that new strand of RNA. After transcription, the RNA is sent out.