On the right is a maranta, probably Maranta leuconeura. On the left is what I'd guess is a date palm (Phoenix sp.) - could be something else though.

On the left might what is called around here in N. Texas a Cyperus. Loves water, can become invasive in this area. we just dug it all out. Too hard to control.

Being a computer cretin, I couldn't see your images. However, if the ID of Maranta is correct - the plant possibly folds its leaves up at night (a prayer plant).

They need even moisture and good light: a west window could be ideal.

According to one source, you can keep them in pure sphagnum moss. They prefer a lean diet and don't feed it in winter. Each month liquid feed with a 20-20-20 brew. (20 parts each of Nitrogen, Potassium, and Phosphorus). Follow the instruction strictly because too much could either burn your plant or kill it. Cram it into the smallest pot you can and spritz it early in the day.

When you have taken it from the florist's container and repotted it, then get a waterproof plastic dish, put some pebbles in the bottom, and put in about half an inch of water. Rest the pot on the pebbles. As the water evaporates it will provide the humidity the plant needs. If you have central heating in your house it will do the same for you and your wooden furniture... Your sinuses could thank you.

If it gets too dry, you could find red spider mites are a problem. Put the potted plant in the sink and gently run cold water over it then leave it to drain before returning it to its tray.

If the other one is a Cyperus - it may be happy growing in a vase with water in it and a pinch of horticultural charcoal to keep the water sweet. No soil.

If repotting sounds scary, check with your local garden centre. Some of them will do the job for you and you can watch/learn for the next time.