Hi and happy Christmas. I use a lot of supermarket herbs in the winter. I keep them on the kitchen window sill. I think the secret is making sure that they are moist before taking the sleeve off. But not too moist. It can be a lottery as you don't know where they store the pots before putting them on display. If the coriander is very tall then leave the sleeve in situ.

You could always cut all the top growth off, chop and freeze in ice cubes to use... Supermarkets are not the ideal place for any herb or spice to grow :(

Thanks,I sometimes freeze bunches of Coriander but it's not ideal. I'll try the windowsill trick Barbarak.

As an indoor plant, Coriander needs bright light, and cool conditions. And, as Barbarak and Moon_Grower say, it is best to get the plants the day that they arrive from the grower, since spending time in the produce department will weaken them greatly.