"Cloud" means a lot of different things to different people, as does a "cloud server", so you'd need to be a bit more specific about what you want to actually do. However, for something like sharing files over the Internet, one option would be using something like owncloud to host files. I've not done it personally, but know people who have.
There are a number of tutorials around, take a look at :
https://blog.adafruit.com/2014/11/21/12 ... spberrypi/
Although this will work fine for personal use, it's not particularly scalable due to the relatively limited resources of the Pi. A "real" cloud system would be able to automatically scale the various resources such as CPU, network bandwidth, storage IOPS in response to user load, scaling them up during busy periods and down when demand falls, which is why providers like Microsoft with Azure, Amazon with AWS and others have heavily invested so much in building massive infrastructure and software stacks to support "bursty" loads.
The whole idea of cloud is to only pay for resources when you need them, rather than have expensive servers sitting idle for a lot of the time, with no upfront investment needed for hardware, which is why they can be very attractive for tech start-ups. The data centers tend to have very reliable power sources, networking, cooling and security, something that is quite expensive to do from scratch.