Kim, probably the single most important part of being successful with plants is to find out what kind they are. It's not possible for anyone else to offer truly helpful advice without knowing what kind of plants they are.

I'd suggest that you take simple digital pictures of your plants and post them in this forum or the Name This Plant Forum.

Then, you'll be able to look up all sorts of information, as well as allow us to properly assist you.

But even without knowing what you have, I will say that plants need water.....AND there needs to be a hole in the bottom of the pot, so the excess water can drain out. When the top of the soil feels slightly dry-ish...water until water runs out the bottom...leave in the sink until it stops running out.
Linda C

Sometimes, when plants are sold as gifts, they are potted into quite small containers. By the time they come to you the roots of the plant may have completely filled the pot and have nowhere else to go.

You can check this without harming your plants by gently removing the current pot. This is so simple to do but it might not be so easy to explain!

You need to be able to make a cup of your hand, leaving a gap between your fingers to let the stems and leaves through - and turn it upside down so you can take off the pot to look before you slide the pot back on.

If there are white or brownish threads coming through the hole/s in the bottom then the plant needs a bigger pot and some new 'soil'. You may well be able to buy a 5litre bag of potting mix at the supermarket and a couple of pots about 5cm wider than the current size.

If the entire pot and plant feel very light then it's water you need and lindac has described exactly what to do.

Cutting off - and before you do. Look down among the leaves to see if there are any new buds emerging. When you snip off a stalk that has finished flowering you need to do so just above the new buds so they stay safe. Use strong scissors for a clean cut.

Look at where your plants are sitting. Do they get hit by late sun on a windowsill? Are they in a draft? Both of these situations will cause most plants to brown off.

I'm wondering if the 'daisy' could be a Gerbera. If you google on that you'll probably get more information on how to keep it (provided that my guess is correct).

rhizo is right, too. A picture would be really helpful. We'd know if you're struggling with a plant that needs to be outdoors for best performance - or a houseplant.

If I need to add anything to these great advice, it is very important to remove the plastic wrapper around the pot. they block the drainage hole and I've seen many people keeping them on. so that goes to trash the moment you receive any potted plant. of course depending on the kind of plant most brightly flowering ones probably need full sun. even the shade plant needs some sun to survive. so the daisy looking one need to be in the sunny window sill . and always away from the air conditioner.

I am guessing if you receive them as a gift from a florist they are probably house plants. It's a good idea to repot them. with new potting soil and slow release fertilizer.

Some plants have a short life and are not meant to last, or keeping them going is too much fuss to be worth it. Pointsetta, easter lily, florist's hydragea are amoung those. Other plants are meant to be kept as house plants but will vary in the amount of water, sun and fertilizer they need. Yet other plants can be enjoyed for a while indoors but then will need to be planted outdoors if you want to keep them longer (example mums). So you can see that you really do need to know the name of the flower to know how to care for it. Most flowers will have a name tag, if not, ask the giver for the name of the plant.

Spring bulbs are one shot deals, enjoy them then throw them out. Since you talked about leaves and flowers dying, I suspect the flowers you had were spring bulbs, perhaps hyacinth and anemones. Once these die back, they are finished.