I was totally unprepared for this and I need some quick advice. There are 2 eggs in my leopard gecko's enclosure. I don't have anything in there for the female to lay eggs in. I know I must mark them and then remove them from the enclosure, but how exactly? They look really soft and fragile. I am sending my boyfriend to home-depot to get some supplies because she is trying to dig still. I told him to get some soil without those little white things and fertilizer free, vermiculite, and some pearlite. Am I on the right track?

Here are some pics. The eggs are stuck together and stuck to a rock.

Should I leave them like this?

Here is another angle. This pic was taken from directly above, looking down.

Do you have a male in her cage that she mated with? If not they would be infertile. Let me know if they would be fertile and I could give you some instructions.

Yes there is a male in the tank with her. I should have known. That is what all that dancing was about. This is her first clutch, my first clutch too. She won't stop digging at the carpet. Is this normal? Any advice or instructions would be great thanks.

Judging by the pictures and depending on how long ago they were laid they may not make it, but its always worth a try to save them.
For my eggs I use the bed a beast. Make sure it is moist but not so much that it has little puddles, otherwise you have to worry about mold forming. I use my finger to make an indent in the bedding so that when you place the egg it is half ways up the side. It is very important that you mark the top of the eggs so you know how they were laid. It looks like you already did this with the egg that is on top of the rock. For the egg that fell off I am not sure how you will judge what is the top. Since they are stuck together I would suggest trying to leave them like that otherwise if you try to separate them the egg may tear. Once you get them placed in the container seal it up and find a warm place for them that stays above 78 degrees and make sure its an area where the temperature will not fluctuate alot. They need to stay at a pretty constant temp. but a difference of 3-4 degrees should not harm them.
You can also check out the caresheet it has a lot of good info and may have some that I left out. But this should help you get started.

I just noticed in your post you have of your new male that you got him about a week ago. If this is true then that would not have ben enough time for the eggs to be fertilized by him. How long have you had the female?

I got her in mid-August of 2004. Here are some pictures that I found of when I first got her. She was really skinny. You can see how rapidly she changed into a beautiful, healthy gecko.
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HI Ssativa

If the eggs are soft, like half filled water bottles....then they are infertile.

They only lay a maximum of 2 eggs at a time (if they are healthy.....as it is with your's, congrats). My geckos always lay their eggs in their moist hide and they do so at 2 wk intervals.

check out our care sheet http://www.herpcenter.com/showthread.php?t=2731

Okay. One egg, the one on the top, is squishy soft and the one one the bottom is firm. I'm guessing this means that the top egg is either infertile or bad. Is it possible for a leopard gecko to lay one fertile and one infertile egg? If so, should I attempt to remove the infertile egg so that the other egg doesn't go bad?

If the male you just purchased is the only male that has been with her they are going to be infertile. It takes 4-6 weeks from the time they mated to lay the first clutch, and as herpmom said they lay every two weeks after that.