Located on Slovenia's major East-West railway line, Celje sees more traffic and thus offers more frequent connections than you would find on a less opportunely placed city. That said, train travel in Slovenia, especially when coming and going further south in the Balkans, is not comparable in terms of speed with that in larger (and flatter) countries - although the scenic views are often more than enough to make up for it. A trip to the capital Ljubljana takes anywhere between one hour and an hour and 45 minutes, with the faster trains costing noticeably more. In the other direction, a train to Slovenia's second largest city, Maribor, takes between 45 minutes and one hour. For the short trip to nearby Laško, trains are far more frequent than buses and take only 10 minutes.
The station itself has sufficient, if not overwhelmingly luxurious or vast, facilities, and is conveniently positioned across the street from the old town, within easy walking distance of most hotels and restaurants. Aside from the ticket office (open 05:00-21:00 Mon-Fri, 06:00-21:00 Sat-Sun) and a small railway information desk (open 06:00-17:30 Friday to Saturday), there are a handful of self-service lockers, a couple vending machines and the requisite railway station coffee bar. If you find yourself stick waiting for a train during the wee hours, your best bet for a bite to eat is a few blocks north at the main bus station.