The reaction proceeds in two main steps:

1. Diazotisation: Aniline (a primary aromatic amine) reacts with cold nitrous acid (prepared in situ from $NaNO_2$ and $HCl$ at 273-278 K) to form benzenediazonium chloride.
2. Coupling Reaction: The benzenediazonium cation is a weak electrophile. It undergoes electrophilic aromatic substitution with the highly activated N,N-dimethylaniline ring. Due to steric hindrance caused by the bulky dimethylamino group ($-N(CH_3)_2$), the coupling predominantly occurs at the para-position of the N,N-dimethylaniline ring.

The resulting coloured product is a yellow azo dye named p-(N,N-dimethylamino)azobenzene. Its chemical structure is $C_6H_5-N=N-C_6H_4-N(CH_3)_2$.