Once everything else is done, the assembly is fairly straightforward...
Insert the LEDs into one end of the plastic holder you made and the card into the other end.
Put the leads from the LED around a battery and slide the battery up so that it is nearly touching the LED itself. I snipped the ends off the leads of my LEDs with scissors to make them a bit shorter because they were a bit long and I didn't want them touching an of the other metal in there.
If you are worried about the life of your LED, make a pull tab to keep the light from turning on until you're ready.
I bought a couple of those old plastic covers you could get for a school report from Office Depot. It's a thin clear plastic and it's nice a smooth so it slides out easily. When you're ready to insert your LED into the clip you simply place this tab between one of the leads and the battery, leaving some of the tab sticking out so that you can pull it out when you want to turn it on. I use a piece of paper in the picture here instead of the plastic, but you get the idea.
When you close the clip it should be right at the top of the battery where it meets the LED. The LED should light up without flickering unless you have a tab in. If you use the tabs make sure you pull a few out after assembly just to make sure you're inserting them properly.
That's all there is to it. Best of luck on your DIY wedding!