Maintaining your seat post does not require you to clean each time you ride or even once a week. However, if you are riding several times a week, it is a good idea to remove it and clean it once a month. I have seen seat posts frozen in the seat tube because of rust and corrosion. You may not realize it, but it is a definite sweat magnet. And sweat = rust on certain parts of the bike depending on the material used. Obviously, during the summer month's this will warrant keeping an eye on things. However, if you are spending time on the stationary trainer during the winter months, the sweat factor is very real.
1) To check for any rust build-up, remove your seat post. Before you do so, mark your spot with tape. I have chosen a blue masking tape for visibility reasons. This tape will not hold. I normally use black electrical tape.(more:www.carbonbikeoem.com)
2) After loosening the seat post binder bolt, pull out the post. Wipe it down with your rag. You will probably notice the copper color of rust on the rag. After wiping it down, cover the post with grease below your mark.
3) Then slip the post back down the seat tube and tighten the binder bolt. There will be some grease that will gather at the top edge of the seat tube. Just wipe it off.