If you are applying syrups or glazes, after brushing the tops of the cakes with syrup, and leveling them if necessary, the bottom layer of each tier should be inverted directly onto a cardboard round of corresponding size and then brushed with more syrup.
Once syrup is applied to a cake, the cake becomes much more fragile and also sticky, making it more difficult to slide the top layers onto the bottom layers. For the top layers, I find it works best to apply the syrup to the top and bottom of the cakes, and to allow them to cool completely, which will help to firm them and flatten the tops. Then I invert the cakes to level them, if necessary, and reinvert them onto plastic wrap, coated lightly with nonstick cooking spray; nonstick aluminum foil—lined disks; or open-sided baking sheets (I often use the nonstick bottoms of tart pans). You will be better able to slide them off the sheet onto the frosted bottom layers.