protein synthesis

Transcription takes place in the nucleus where DNA is transcribed into premature mRNA then into mature mRNA after splicing of introns, poly A tail addition and 5' cap is added, then the mRNA is transported to the cytoplasm where translation takes place either at the ribosome or the rough ER...

free ribosomes not bound to the ER can do protein synthesis too and their proteins are used within the cell while membrane bound ribosomes that are attached to the ER (termed rough ER) can also do protein synthesis and their proteins produced can be used within the cell or out of the cell via exocytosis...

Hope that helps...

Proteins are often synthesized on ribo's on the ER (mainly transmembrane proteins). Proteins translated in the cytoplasm are often soluble proteins. Transcription is always in the nucleus because DNA does not leave the nucleus.

Another thing to note is that because prokaryotes (that is, bacteria; not sure about archaea) lack a nucleus and an endomembrane system (ER), transcription and translation both take place simultaneously in the cytoplasm. In other words, even as the polymerase is transcribing mRNA, ribosomes are attached to that same mRNA and are transcribing polypeptide chains.

Looks something like this:

Also with prok's, genes are often polycistronic (more than one gene transcribed into one mRNA = multiple proteins) whereas euk's are monocistronic (1 mRNA = 1 protein).