Step 1: Experimental Setup - Meselson and Stahl grew E. coli in a medium containing $^{15}NH_4Cl$ (heavy nitrogen) for many generations until the DNA was completely labeled with $^{15}N$.
Step 2: Transfer to $^{14N$ -} The cells were then transferred to a medium with normal $^{14}NH_4Cl$. They took samples at 20-minute intervals (the time it takes for E. coli to divide).
Step 3: Centrifugation - Using Cesium Chloride ($CsCl$) density gradient centrifugation, they observed that after 20 minutes, the DNA was of hybrid density ($^{14}N^{15}N$). After 40 minutes, there was an equal amount of hybrid and light DNA. This proved that each new DNA molecule has one old and one new strand.