In a eukaryote, transcription takes place in the cytoplasm (prokaryote) or in the nucleus (eukaryote). The transcription is performed by an enzyme called RNA polymerase. To make mRNA, RNA polymerase:

1. Binds to the DNA strand at a specific sequence of the gene called a promoter
2. Unwinds and unlinks the two strands of DNA
3. Uses one of the DNA strands as a guide or template
4. Matches new nucleotides with their complements on the DNA strand (G with C, A with U -- remember that RNA has uracil (U) instead of thymine (T))
5. Binds these new RNA nucleotides together to form a complimentary copy of the DNA strand (mRNA)
6. Stops when it encounters a termination sequence of bases (stop codon)

mRNA is happy to live in a single-stranded state (as opposed to DNA's desire to form complementary double-stranded helixes). In prokaryotes, all of the nucleotides in the mRNA are part of codons for the new protein. However, in eukaryotes only, there are extra sequences in the DNA and mRNA that don't code for proteins called introns.