Most of the big PLC manufacturers like Modicon and Allen Bradley have demo versions of their PLC programming software that you can download and play with. Most of them will run in a simulation mode, but won't actually control a PLC, or may be downloadable only into one of the cheaper PLC's that the company makes. It's a good way to get some practical experience. They also have training classes available.
Architecturally, a PLC is very similar to an industrial computer. A PLC tends to be a proprietary motherboard with its own boot rom and flash storage, where an industrial computer will have removable memory and a socketed flash module (like a disk on chip flash disk). Both industrial computers and PLCs are designed to be significantly more reliable than your standard desktop PC, which would likely die a very early death if you stuck it in a plant. Additionally, a PLC will usually not contain a cooling fan, where most industrial PC's do have a cooling fan, which may limit their reliability in dirty environments. Otherwise, there's no significant difference in a typical PLC and an industrial rated computer in terms of reliability. There are however things like triple redundant PLC's like those made by Triconex which do have a greater reliability. If you were to create a triple redundancy scheme using off the shelf industrial computer parts you could achieve similar levels of reliability.
PLC's historically have usually run their own proprietary operating system, because commercial operating systems would not provide the reliability, features, and small footprint needed. In recent years, commercial operating systems have become much more powerful and robust, and parts have become cheap enough that a cpu board can be made which can run a generic operating system and have enough resources left over to run the applications code as well.
