What is the difference between code, codon, and anticodon?

The codon is a set of 3 nucleotides that can be read to convey a message in your DNA. It can be a code saying to "start" the process of protein synthesis, or "stop" it, or to encode for an amino acid - the building blocks of proteins. 
The DNA is read, and proteins are made by DNA Polymerase (simple version here, it is more complicated, but this is the gist of it) travelling down the DNA. As it travels, it reads the nucleotides and builds a chain of amino acids, that corresponds to the information gleaned from the DNA. 
So, the codon is only on one side of the DNA, and there are 2 sides. In order to be able to keep the DNA safe, and package it well (and loads of other reasons ) there is a complimentary strand. The nucleotides that make up DNA are A, T, C, and G. A links to T and C to G, and vice versa. 
So if your DNA strand's codons read "AAG AGG TCA"
Then the complimentary strand will read "TTC TCC AGT" the three codons on the complimentary strand ARE THE ANTICODONS of the codons on the strand being read (aka "expressed").
So a codon and an anti codon are made of the same things, it just is a matter of which is being actively expressed. Now, this gets insanely complicated when you learn more about reading frames! Not only are there those codons, but if you shift and start reading the "code" either one nucleotide earlier or later, it completely changes the message.