Artifacts appear when I use the subsurf modifier I'm (almost) a complete newbie in Blender. I thought that modelling a greek column would be a great exercise for me. My mesh doesn't look so bad, but when I subdivide everything, some strange artifacts appear :(

Here is an example:


Also, here is a link to my .blend file, so you can see the mesh:
.blend file
Could you give me some advice how to remove those strange things? :/
Your problem is that along the object you have large and ugly ngons (polygons with more than 4 vertices). Ngons don't work so well with the subsurf modifier.

Use quads instead to connect all of the other vertices, that will give you a nicer edge flow: