During translation, which is the process by which proteins are synthesized at the ribsomes, activation first occurs. This is when the correct amino acid is joined to the correct transfer RNA (tRNA). When this occurs, translation proceeds. When a tRNA has an amino acid linked to it, it is charged. It can then bind to the mRNA molecule in the transcription based on linking with its complementary codon. Next, another tRNA binds to the next codon in the mRNA and its amino acid links to the previous one, forming an elongated polypeptide. This will occur all along the transcript as tRNA bring the appropriate amino acids to the growing polypeptide chain at the ribosome. Eventually, this process will cease when the stop codon UAA, UAG, or UGA is found in the transcript. At this point, no tRNA can recognize it, and a releasing factor initiates the release of the polypeptide chain from the ribosome.
In addition to trophyhinter1's answer
It is true that a stop codon is not recognized by tRNA, but the factor that actually stops the translation process is a release factor. A release factor is a protein that has the same capability of tRNA to recognize mRNA codons, but instead of adding an amino acid to the polypeptide it adds a water molecule, which hydrolyzes the bond between the polypeptide chain and the tRNA, releasing the polypeptide.
Source: Campbell Biology Seventh Edition AP edition