I'll try to simplify this as much as possible (although it will be lengthy, but I'll try to be as clear as possible). We tie dye all the time.
First, did you open your tie dye kit? There will likely be instructions in there for not only how to prep your fabric (i.e. does it need to be pre-washed? wet? dry? we always pre-wash ours, and have them damp when we actually tie die them), and most likely it will also have an instruction sheet with some basic/common tie dye rubber banding patterns to follow. I learned many of our techniques simply from looking at those instruction sheets. If your kit doesn't include a technique sheet, you can certainly google simple tie dye patterns. **Ok, not so much. I just googled it to find you a link, and it is not as easy as I expected to find 'simple' tie dye patterns with simple instructions to follow. If you don't have an instruction sheet in your kit, pm me and I'll give you some specific instructions on basic rubber banding patterns to create some great looks.
Make sure you get an extra bag of different sized rubber bands to be sure you have enough on hand, and of varying sizes. Be aware that some dyes require salt in hot water, others just require water, so again, read your dye and see what it calls for. If you need salt, you'll want to make sure to have enough on hand. And get a bag of latex gloves for everyone to wear. Do have the kids bring/wear old clothes. They WILL get dye on their clothes, and bodies, etc. Definitely do this outside, if you can...
You can tie dye one of two ways, by squirting the dye onto the rubber banded shirts, or by soaking the rubber banded shirts in a bucket with the dye in it. We do both. If you want multiple colors on one shirt, you have to squirt the colors on with the bottles provided. With this method, you want to try not to overlap the colors, and you need to try to soak through the layers of the fabric to avoid too much white left on the shirt, although some is white is necessary to create the effects, but any spot of fabric under a rubber band will remain white. There does not have to be any rhyme or reason to 'where' you squirt the various colors, any design will create an interesting effect, really.
If you want to simplify things, and do single color shirts, you will need to get some buckets (we've used large salad type bowls or large soup pots that we have in the house - you don't need huge buckets unless you plan to have more than a couple shirts in any given color at a time.) If you are soaking, you need to make sure that the dye is squeezed into the fabric well (we often do a pattern where all you do is crumble the shirt up into a tight ball, and rubber band around it to hold it together, then soak the ball in the dye... this creates a cool effect, but you have to make sure to really squeeze the ball in all directions to squeeze the dye into the innermost part of the shirt ball, or you will get large white patches on the finished shirt where the dye didn't get in, which you wouldn't want.)
We used to leave our shirts overnight, but due to a need for instant gratification, we stopped doing that! We'll let them sit for a couple hours, then rinse, and honestly, I don't notice a bit of difference in the ones that sat overnight, to the ones that sat for a couple hours, in terms of colorfastness or intensity. With this being a party, I'd say the girls will want their shirts done rather quickly, so I don't think you need to let them sit overnight.
After our shirts have sat for a couple hours, I'll take them to the washtub and remove the rubber bands and give them a thorough rinse with cool water until the water runs mostly clear (it's near impossible to get all the excess dye out without washing in the machine.) Be prepared to do a LOT of wringing. My hand and forearm muscles are always sore the day after we tie dye! LOL
When we tie dye, I get a plastic table cloth or tarp (dollar store) to keep dye messes to a minimum. You will need a place to lay the rubber banded and dye laden shirts while they set. Do not let shirts with different colors touch one another as they set, or as you rinse them, or you will get color bleeding. Also be aware that any dye on your gloves will transfer to the fabric when you touch it, so if you just had your hands in red dye, and pick up a white shirt that you want to dye blue, you'll have purple spots on that shirt. The shirts are very sensitive to 'catching' the dye. Also, when you open the dye packets, I'm assuming it's a fine powder, that powder will transfer to the shirts as well... say, if you open the packet on the counter, to add to the water, and some dye dust lays on the counter, if you set a damp shirt on that fine, almost invisible powder, you will see that it instantly picks up that dye. So you just want to be cautious. (Of course bearing in mind this is a fun craft project for kids, not something that needs to be perfect to sell or something, so little snafus are no big deal.)
Once you have all your shirts rubber banded, with dye on them, lay them out on your plastic cloth. Let them sit for a couple hours. Rinse well. Wash like colors together in your machine with laundry soap. Dry. Voila! Tie dyed shirts! Such a fun project. We love it and do it a couple times a year. My son is 5 and loves to do his own...
Good luck! We love tie dying! If you have any specific questions, please pm me!
Added: I like the idea of using plastic grocery or ziploc bags with the girls names on them to keep the shirts from accidentally coming in contact with one another, keep the mess contained to the bag, and to keep them from claiming someone else's shirt!