There are three different ways in which you can avail cloud computing services. They are public cloud, private cloud and hybrid cloud.
1. Public Cloud: These are services provided and managed completely by third party vendor over the internet. Anyone can avail service from these vendors. All the hardware or software resources that you wish to avail will be managed completely by this third party vendor.
Microsoft Azure is an example of public cloud.
2. Private Cloud: These are services used exclusively by a single business or organization. These are services that are on local network and not public. It is hosted within the organizations site or a third party hosts it locally.
3. Hybrid Cloud: This is a combination of public and private cloud. Some resources are held locally and some are on public cloud. This gives more flexibility to your business.