There exist several options to obtain a MOODLE platform:
Institution’s own Server
You have to download the MOODLE installation files, to install MOODLE, and to configure the system.
MoodleCloud
This is maybe the simplest way to get a Moodle platform. It is a cloud-hosted solution for your learning environment provided directly by the Moodle main team (Moodle.com). They offer various packages & plans (including a free one) to meet your specific needs and requirements (see link). You can upgrade or downgrade your plan at any time.
Hint: For a maximum number of 50 users the use is for free.
The main disadvantage of Moodlecloud is the fact that it uses the standard Moodle configuration and you cannot install additional, third-party plugins or themes to adapt and customise the platform.
Link: MoodleCloud
Moodle Partners
These is a network of certified MOODLE experts. They act as service providers that are certified by the Moodle HQ to provide Moodle services for your school, institution or organisation’s online learning environments. They can not only install the platform for you, but also provide other services like technical maintenance, periodic backups, upgrading, teacher training, etc.
Moodle Partners pay a portion of their income to Moodle HQ in the form of royalties to help keep the Moodle project moving forward helping ensure the ongoing development, support and maintenance releases of Moodle.
Third party hosting services
You can also buy your own internet domain and a hosting service, that is, either a dedicated server for your exclusive use or a server shared with other clients.
Offered by the school authority
In some European countries the school authorities offer a pre-defined and installed MOODLE platform for their schools.