Compared to most plants, succulents are relatively easy to care for. They will last years, or in some case decades, if you look after them properly (and you can't say that about your flower delivery!). They need a fair bit of light, not too much water and a feed every now and then. Even if you are terrible at caring for plants, these should last weeks (if not months) before they start to show signs of your "black" thumb.
What are the care Instructions?
Succulents generally like lots of light, but not too much direct sunlight. So be careful to protect them from the late afternoon summer sun. They will also do very poorly if left in a dark position for very long.
They like a good watering in the warmer months, but only once the dirt has completely dried out from the last drink (perhaps once a fortnight to every month). And they need very little water in winter (just once every 6 or so weeks is fine). When you do water them in winter, water sparingly. Less is definitely better than more!
Finally feed them a succulent food once a year and they should thrive.
My plant looks to be dying - where did I go wrong?
If your plant starts to look unwell, the most likely cause is that you have overwatered it. Even if you think your plant is thirsty, unless it has been months since its last drink, the drooping plant probably has been overwatered and may even have rotten roots. It may not be salvageable - but you can try drying it out, perhaps pulling it from its pot and replanting into dry soil, before putting it in a dry position with a fair amount of light and leaving it for a few weeks to see if it recovers.