Denise,
Let the foliage die naturally. As long as it is green, it feeds the bulb for the next season blooming. If it is already yellow/brown, you can cut it as close to the ground as you want. I prefer to leave a piece of stem about 3-4" long to remember where the bulbs were planted.

My Red border Asiatic Lilies has all turned brown and look horrible. I don't know what to do with them. I planted thirty bulbs last fall and they all came up and got a few to have red lilies on them. Now they look awful. I am lost with these lilies. Help please!!!

It sounds like they have gotten too much water, ladytexan. That's been my favorite way to kill lilies. :oP