Hi zap,
They only need high humidity if it's really dry, otherwise they will be fine with no humidity dome.If it came with a humidity dome, you will need to harden them off to lower humidity by lifting the dome a little each day.
You should give the flytrap full sun.If the the sundew is a drosera adelae,give them indirect sun.
If you follow these instuctions and keep them in standing water, you shoud have a happy plant.

zapcory2:

Follow carnivorousplants advice. It is a complete myth that Venus Flytraps and sundews need high humidity. They can adapt to relatively low humidity, I believe somewhere as low as 30%, with ease just by opening the humidity domes or terrariums they might be in slowly. Take a couple of weeks to wean them off of the high humidty by opening the cover about 1/4 to 1/2 inch every three days until it is open about 2 or more inches and then take it off completely. The plants will make tougher leaves.

As for the Venus Flytrap, as indicated in the previous post, they need high levels of direct sun. If you bought it in a hardware store, you need to adapt it to ultraviolet light slowly too. Each week, place it in a brighter window, like a morning sun window on week one, a all day sun window on week two, and outside in full sun on week three. It will get some leaf burn even then, but it wont be as bad as if you threw it out in full sun all at once. It's new leaves will be adapted to high light levels and will grow more quickly and more colorfully.

Check to see what type of sundew you have. Drosera adelae cannot handle full sun and is a tropical, so keep it inside in a morning sun window about 6 inches or a foot back to keep it from getting burned. It likes bright light, just not direct ultraviolet light. The window will cut most of that, but you also dont want it getting too hot either.

These are D. adelae grown under florescent light of 12000 lumens 5 inches from leaves, note the reddish leaves as well as tentacles.

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This is another commonly sold sundew, D. capensis. It can take up to full sun but does not require it and is a tropical. It can be grown easily indoors in a sunny window next to the adelae or under florescent light as well.

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If those are not your sundews, look around and do some research to find out what it needs to survive.

Since you live in a desert, if it gets over 100 degrees in temperature, you will need to protect the Venus Flytrap from that as that is the real killer. They can tolerate temps of about 20-100 degrees in the wild. In your case, I would place the Flytrap in an oversized tray that is about as high, or a couple of inches higher than, the pot and fill it with an inch of water. That will trap some extra humidity and allow the plant some air. Flytraps in closed spaces often succumb to root rot and mold as their leaves grow floppy and weak. In an open tray, they can get open air, more light, and can soak up lots of water from the tray as needed through the pot drain holes... your pot does have drainage doesnt it? Some stores sell Flytraps in pots with no drainage... bad idea, it promotes root rot as water just sits stagnant in the pot bottom and keeps the plant from getting bottom watered in trays. In any case, if that desert climate is too brutal for the plant, you might have to resort to inside growing in a window with a good florescent 40 watt shop light as a supplement. Flytraps need a huge amount of light to grow well.

This Flytrap is being grown in 50% humidity in zone 9 Texas. Definitely not a rain forest or bog in sight here.

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Good luck with your plants.