I would like to know the detailed procedure of how scientists in earlier time were able to locate genes like how we were able to locate Huntington gene in 1983?
The earliest genome maps were constructed from Escherichia coli by abusing conjugation of special Hfr-mutants. I'm assuming you are somewhat familiar with bacterial conjugation - the process of transferring genetic material between bacterial cells.
Usually, only mobile plasmids are transferred. They carry the necessary tra-genes for the construction of the sex-pilus, replication and transfer system. They also need the oriT-site (origin of transfer), at which transfer is initiated. A famous mobile plasmid is the F-plasmid.
Some mutant cells integrated the F-plasmid into their main chromosome via recombination. Thus, they are able to transfer their whole genome to a recipient cell. These strains are called Hfr-strains (high frequency of recombination) and they were used intensely in early genome mapping.
They discovered, that it takes roughly 100 minutes for a Hfr strain to transfer its entire genome to another cell. By interrupting conjugation (e.g. by vigorous shaking) the transfer was interruped and the genome could be divided into sections by transfer time (10min, 20min, 30min and so on).
The function of the genes (or genome sections) was revealed by mating Hfr strains with defective mutants. If the mutant was unable to grow on saccharose for example, several conjugation experiments with different mating times were conducted. When a mutant was able to grow on saccharose again after mating, the transfer time was checked. If the strain was able to grow again after 30 minutes of conjugation, but not after 20, they knew the genes necessary for saccharose growth lay in the 20 - 30 min region.
It took a painstaking amount of experiments with a wide range of mutants to construct the first map of E. coli genes, but it was achieved before even the nucleotide sequences were known.
Just to complement Pythagyros.
Sequencing and bioinformatics were already around in 1983, actually Frederick Sanger and colleagues published their automated method of sequencing (Sanger sequencing) in 1977. They published the complete sequence of the bacteriophage φX174. Other methods of DNA sequencing had been around since the first one in 1970 established by Ray Wu.