How is a sequence of amino acids produced from a mRNA transcript?

mRNA enters ribosomes, where it is read in groups of 3 bases at a time (ex: AUG, UUU, GAC), these groups of 3 are codons.

tRNAs with amino acids attached are pulled into the ribosome. These tRNAs have what are called "anti-codons" that are complimentary to the codon. 5'AUG3' for example would have an anticodon of 3'UAC5', and carry the amino acid methionine. Each group of 3 would tack on another amino acid to the growing chain.

The mRNA keeps sliding through the ribosome until a stop codon is signaled. Then a stop factor stops the translation process, breaks up the ribosome and you have a complete polypeptide.