I won't get into the mechanics of the enzymes involved and such, but what happens is this:
1) DNA is transcribed into mRNA in the nucleus. There are particular codons that the enzymes are looking for that begin the transcription.
2) The mRNA travels to, and attaches itself to a ribosome, which is either free floating in the cytosol or attached to the RER. There, the nucleotides are read from the start codon, in three letter sections, each of which code for a particular amino acid (some amino acids have multiple codons that code for them).
3) tRNA brings amino acids from the surrounding cytosol to the ribosome, and attach them in the order coded by the mRNA.
4) The amino acids are bonded together by peptide bonds, like proteome said. They are in a long linear chain, which is the primary conformation. The conformation to secondary structure is usually spontaneous, based on the interactions between the amino acids within the polypeptide. However, when going to the tertiary and quarternary conformations, there are usually larger proteins called chaperones that assist in the folding.
This is a rough outline. For more details, just ask. I don't know what grade level it's for, but I, or someone else here, can extrapolate for you if there isn't enough detail.