First of all, protein synthesis is translation not transcription. So I will take it that you just typed this wrong.
So, translation of mRNA into the protein ends at a step called termination. Termination happens when a stop codon in the mRNA (UAA, UAG or UGA) enters the A site. These stop codons are recognized by proteins called release factors which fit into the P site of the ribosome (note these are not tRNAs). These release factors mess with the enzyme that normally forms peptide bonds - and this then separates the chain from the tRNA and the newly made protein gets released. the small and large ribosomes then separate from eh mRNA and can go do another round of translation with another mRNA (good recycling!!).
