Shotline, my guess is that your plant is a tillandsia, which is an epiphytic plant like a bromeliad or an orchid. If your plant is attached to a branch, you can't water it most efficiently, which is to soak it in water for a few hours every week. I think your misting method is good, but there are 2 things to be conscious of.
First of all, is the plant in a bright or dark spot?
Second, is this spot warm or cold?
(I know, these are generally connected, as is your watering regimen.) If the spot is very bright and warm, mist it frequently. If it is cold, or gets cold overnight, you will want to be more sparing with the water. If the center of the plant is cold, the activity there, where new cells are produced, will slow down. Excess water will cause it to rot.
Your indications of what is going on is how the dead plant looks. If it is kind of splotchy and wet when it has died, it was overwatered. If it is dried out, it was underwatered.
If you can, find your plant a bright, warm spot -- not in the direct sunlight -- and it should thrive with the occasional misting; a few times a week should be fine.
Shotline said:
I often buy tropical plants which are attached to wooden branches (I hope you know the kind I am talking about).
They always die off fairly quickly because I cannot figure out how to water them. I have tried misting them, pouring water over them, not watering them but nothing works.
What is the proper way to care for these plants?
No questions here. I just wanted to show them off. You call yourself the plant pimp, I gotta show my bling. 
(in reference to a pic I previously posted)
