Is traveling from Uyuni (Bolivia) to San Pedro (Chile) easy? I've read there are some problems on the border.
Also, should I wait to arrive in San Pedro before to buy a guide tour to see his sights, or should/can I buy such package in Uyuni?
You pretty much will have to go on a tour. It's through a national park area, and in addition to that, requires extensive knowledge of the area - there aren't many roads as such. So you'll go on a tour, and they'll guide you through the border.
So in that regards, yes, it's very easy. You join a tour, and follow their instructions :)
I can recommend Tierra Mistica, although our guide only spoke Spanish, it was a very enjoyable trip (the tour at least, Uyuni didn't go so well for me, but that's a different story).
Tours on the Bolivian side are significantly cheaper.
On your own, it's easy to get from Uyuni to San Pedro, if a bit time consuming. Public buses run four times a week between Uyuni and Calama, take 7-9 hours, and run by day. In Calama, it's easy to get another bus to San Pedro.