How do people actually find codons in a DNA transcript just by looking at it?
Codons refer to sequences of nucleotide triplets that translate to amino acids. As you know, polypeptides are translated at the ribosome using a messenger RNA (mRNA) blueprint produced by RNA polymerases from the DNA.

DNA consists of four nucleotides: adenine, guanine, cytosine and thymine. Thus, DNA sequences read, for example, ATAAGC. RNA, however, replaces thymine with uracil. So to transcribe the above DNA nucleotide sequence into mRNA would result in UAUUCG. 

The mRNA may also get spliced into various isoforms coming from the same gene. In short, it may be difficult to determine the gene product from the DNA sequence.

Does that make sense?