i place the cake on a cooling rack then slide it onto the cake. you can also freeze the layer for a while then it will hold up and you can just pick it up and place it on the cake
This is the reason that I hate doing sheet cakes! Sorry - I have no advice for you except - GOOD LUCK! 
Slide a cardboard under it and then slide it off the cardboard to transfer. I cover the cardboard in press & seal and clean & reuse.
Thanks christapaloma for the press & seal suggestion--I also use a cardboard, but wanted to reuse it
I had the same problem this weekend with a 2 layer round 16 inch cake... I cooled the second layer on a large Wilton non stick cooling rack. The cake as it cooled stuck to the cooling rack (non stick rack - go figure!). I then inverted the cake onto a large cookie sheet (it is one of those flat cookie sheets with no sides) and tried to slide it on top of the bottom layer. Well, it would not slide easily... I guess I will try lining a cardboard base with the plastic wrap for next time. Is there anything else out there that anyone else uses? I thought maybe a sprinkle of powdered sugar on the sheet might help but did not try that...
I would say use the tilted spatula and then slide a board under it... or put the board on top and flip them over... might need an extra pair of hands!
One of the comments from MessiET was that their cake was sticking to the cooling rack. I read somewhere that you can put a paper towel down on the cooling rack before inverting the cake. This helps absorb some of the moisture and it also helps by not leaving cooling rack marks on the cake. Then after it's cooled you can put it on a cakeboard and slide off onto/or next to the other cake. It's worked for me so far.
i use and always used a cookie sheet . it works better than cardboard because the cookie sheet is stronger and wont bend i dont move my cakes if its not with the cookie sheet (thin one ) i move the 18x12 or 13 two of those together to make a big full sheet
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