Firstly, the relevant DNA has to be unwrapped, because it is stored in a very tightly wrapped-up form to save space in the cell. The Hydrogen bonds between the two strands are broken, and the coding strand is exposed.
An enzyme called RNA Polymerase, with the help of a few other small proteins called Transcription Factors, binds to the exposed section of DNA. It then moves along the DNA section, joining free nucleotides together in a sequence complimentary to the nucleotide bases of the DNA section. G pairs with C as usual, but as this is RNA, A pairs with U. RNA Polymerase moves along the DNA strand, creating a whole complimentary RNA fragment of the gene in question. This process is called Transcription.
Once the gene has been Transcribed into mRNA, it is then ready for Translation into a protein. It is transported to a Ribosome, after some modifications are made. The Ribosome is an organelle made of RNA itself - and its' job is to create proteins from an mRNA code. The coding strand of mRNA travels through the Ribosome. While it does so, tRNA molecules, each having a triplet of nucleotides as a binding site, bind to the corresponding triplet on the mRNA (known as a codon) and adds an amino acid molecule to a chain created by the preceding tRNA molecule. As each tRNA molecule adds an amino acid, the resultant polyamine becomes longer and longer. Eventually, once all the mRNA has been transcribed, the protein is ready for packaging and use by the cell.