I just picked this plant up from the store. What is the best way to take care of it? Can I leave it like it is and let it sit in the sun?
On the assumption you mean indoors in the sun, it would be best if it wasn't in full, hot sun all day because it might affect the roots - the glass may magnify the sun's rays and cause burning, and will certainly cause a fair amount of condensation on the glass under the bulb. A little sun is fine though, and yes, you can and should leave it as it is in its container until it's finished flowering. It is not meant to be kept outdoors, in case that's what you meant, although it can be planted outdoors once the leaves have all died back.
In addition to Bamboo's answer, keep the water level to just below the bulb. Don't let the bulb sit in water otherwise it will rot. You may wish to add some liquid plant food to the water to further feed the bulb. Cut off the spent flower head and plant up in bulb compost being careful with the fragile roots. They can then take up nutrients needed and be used next year in the garden.