mRNA binds to the ribosome. The AUG start codon sits in a particular site on the ribosome (the P or peptide site) and binds a tRNA with Met bound to it. The second codon, GAA in this example, binds a tRNA with Glu bound in a second site (the A or aminoacyl site).
The ribosome catalyzes the formation of a peptide bond between the amino acids in the P and A sites.
The dipeptide moves to the P site and another tRNA brings the next amino acid into the A site. Another peptide bond is formed between the second and third amino acids.
This process continues until a stop codon on the mRNA enters the A site. Then the mRNA and the new protein are released from the ribosome and the protein is free to fold into its native structure.