Basil is an absolutely brilliant supermarket herb to buy in a pot for propagation, and so very easy !
Pick off a few stems, about 3 inches in length. Pinch out the tiny leaves at the top. Remove the lower leaves and put them in a pot with water on the windowsill.
They will root in no time, and then you can put them in pots of compost where they will grow into lovely bushy plants.
You can repeat this process with your new plants ad infinitum. The only time that I have failed was during the winter months when the windowsill was too cold, otherwise, a foolproof method. I hope that this helps.