Make sure you have the proper parts and know how they go together. Visually or using your baking pans attach the plates to the pillars and make sure everything matches up and the sizes are correct for your cakes sizes. http://www.wilton.com/cakes/tiered-cakes/separator-plate-cake-construction.cfm for a little more information. You still need to have your cakes on cake boards and the proper supports with dowels/bubble tea straws.
make sure your tiers are perfectly level. If using one plate w/pillars, those pillars are pushed into the lower tier and the plate w/the next tier sites on top of them. YOu must be sure those pillars are pushed in *straight*. What I taught my studenst was to push them in just enough to get them to stand up. Now turn the cake *all around* observing if they are straight. If not, as you push in another 1" or 2" you can push so they straighten. Continue pushing in just an 1" or 2" straightening as you go until you meet the base they will sit on.
If using 2 plates then it is even more important the tiers are perfectly level. Being off just the slightest bit on the bottom makes the cake lean more and more the higher one goes (the more tiers added).
Look through my gallery - there are many cakes using pillars - it might help you understand this post :)
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