Character on moving platform

I spend the last few days making moving platforms in my sidescroller, but when my character gets on them it seems to be afected a little bit by inertia, when I want my character to “be still” on the platform.
And when the character is standing next to a moving platfomr and gets pushed by it, the platfomr clips inside the character and the pushes it.
(Sorry for bad english :s)