How do the DNA modules tell the cell what to do?
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This question is too broad (and also a bit poorly defined). I will try to give few concepts to help you in your exploration of wikipedia articles. If then you have more specific question, we'll be delighted to help you answering them.
In very short...
The genetic information contained in DNA in coded through codons, which are series of three base pairs, there are 4 different base pairs, namely, A,T,C,G. Therefore, there are $4^4 = 64$ but these 64 codons codes for only 20 amino acids (in most species). By analogy you may consider a base pair as a letter, a codon as a word (all words are made of 3 letters) and genes are sentences. But many words are synonymous. The genetic code is said to be redundant.
DNA is a double stranded molecule, which splits in two around a coding region so that a RNA molecule can be created by copying the DNA template. This process is called transcription. This RNA is called pre mRNA. It is then spliced to become a mRNA (messenger RNA). The mRNA exit the nucleus. Two rRNA (ribosomial) RNA (which forms the so called ribosome) attach to the mRNA and tRNA (transfer RNA) will recognize the RNA sequence and paste amino-acids the ones to the others according to RNA sequence. This process is called translation. The molecule that is constructed is a polypetpide (a protein).
The quantity of proteins that are produced can be regulated by various mechanisms at different "moments": pre-transcription, pre-translation, post-translation.
I agree with Chris that this is way too broad a question. But if you want a very broad answer...
DNA is a long molecule consisting of a sequence of 4 different subunits. The sequence of those subunits determines the shape of the DNA, and its shape determined how it interacts with other molecules, based on their shapes.
Computer code doesn't work like that at all, so I think you need to really strongly question your premise that knowing anything about computers is going to tell you much about biology.