The short answer
Supermarket pots contain dozens of seedlings crammed together. Split them into three or four clumps, repot in proper compost, and they will live for months instead of days.
- Split a supermarket pot into three or four clumps as soon as you get it home.
- Repot into larger pots with multipurpose compost, one clump each.
- Water from the bottom, standing the pot in water for ten minutes rather than pouring over the leaves.
- Give them light. A windowsill that gets sun for part of the day.
- Harvest from the top, pinching out growing tips, which makes the plant bush out rather than go leggy.
What will ruin it
Basil hates cold and wet feet. Overwatering is what kills almost every supermarket basil plant, not underwatering, and it happens fastest on a cold windowsill.
Why it works
Those pots are sown thickly for a dense saleable display rather than for plant health. Dozens of seedlings in one small pot exhaust the compost and compete for light within days.
Tipking is general household information, not professional advice. Test anything on a hidden patch first. Full disclaimer.