Cell Nucleus
Here RNA comes into existence as the newly created messenger RNA (mRNA) molecules known as primary transcripts or pre-mRNA. It undergoes some modification before being transported out into the cytoplasm. Modifications include 5' capping, 3' polyadenylation, and RNA splicing. Messenger RNA sequences that are not modified are assigned to the rubbish bin; they are degraded. RNA splicing is where non-coding sequences of DNA known as introns are removed. For many years introns have been referred to as 'junk DNA' - this view is now changing, and they may have some use after all. Only the exons now remain after the spliceosome has gone to work. Each exon codes for a particular part of the protein that is about to be created.
Ribosomes
The workhouse of the cell - this is where the proteins are created. Genes are written in the language of DNA, but for proteins the language is amino acids. So the messenger RNA (which is initially formed as a complimentary strand to a sequence of DNA) has to be translated. This happens inside the ribosomes which are situated in the cell cytoplasm. The process involves another RNA molecule, and it's called transfer RNA (tRNA) and it bears the amino acids which form the protein.
Mitochondria
These organelles are the energy producing power plants of the cell. They have their own DNA and RNA which are separate from the nuclear genetic material.