DNA get's transcribed within the nucleus-->mRNA
mRNA gets shipped out into the cytoplasm.
Inside the cytoplasm, the two subunits of ribosome cometogether and attach to the start codon on the mRNA.
The anticodon of Met-tRNA (the tRNA carrying the amino acid methionin: All proteins start with this amino acid, because this amino acid is attached to the tRNA that recognize the start codon) recognizes this start codon. This recognition allows the met-tRNA to sit within the P-site of the ribosome, leaving the A-site vacant and ready to receive the next tRNA. The next tRNA recognizes the codon of interest and arrives at the A-site. Next, the methionin amino acid gets linked to the amino acid attached to the recently arrived tRNA, which is sitting at the A-site. As a result, the tRNA sitting at the P-site now has no amino acids attached to it, while the one sitting at the A-site has two amino acids attached to it.
Upon consumption of GTP, the entire ribosomal complex moves one codon ahead in the 3'-->5' direction on the mRNA. What's the result?
-tRNA at the P-site moves into the E-site and exits the ribosome complex.
-tRNA at the A-site (The one carrying two AA) moves into P-site.
-A-site becomes vacant again to accept the next tRNA.
This cycle continues over and over again, resulting in elongation of the polypeptide chain.
Keep in mind that throughout this process, the ribosome is moving from the 3' end of the mRNA toward the 5' end, until it reaches a stop codon. At this point, the ribosomal complex falls apart, the polypeptide chain gets released, and the process ends.