The position of a specific gene on a chromosome can be determined by:

To map a specific gene on a chromosome you could sequence the DNA and then from that determine the location of the gene by the sequence (genes almost always start with ATG on the DNA ... sometimes GTG, but that's rare). You'd then find the stop codon and from the ATG to the stop codon is the gene.

You can use a few other techniques including restriction enzyme mapping and hybridization using fluorescent or radioactive probes.