In the nucleus the DNA is transcribed and processed to mRNA which is translated into proteins in the cytoplasm. What happens between the time a protein is made and that when it reaches the cellular organelle in which it functions? How is it transported to its destination?
Mature RNA is translated into proteins by the ribosomes. Ribosomes bound to the ER (endoplasmic reticulum) translate proteins that are bound for export from the cell. Free ribosomes, which are found in the cytosol, are used for structures within the the cell (http://www.brighthub.com/science/medical/articles/110037.aspx)
Proteins made on the ER are sent to the Golgi apparatus, and are packaged there for transport out of the cell. (http://www.ncbi.nlm.nih.gov/books/NBK9838/)
As far as I know, the proteins made by free ribosomes remain in the cytosol and are incorperated into certain organelles or pathways upon contact with specific other proteins or signalling molecules.
Nucleus: DNA transcribed to mRNA. mRNA is sent out of the nucleus and into the cytoplasm.
Ribosome: Site of translation. Amino acids are placed in accordance with the mRNA codon (triplet of mRNA sequences). Folding is done as the protein is formed.
Once the protein is complete, the golgi apparatus is responsible for packaging and exporting it.