It will depend on the cloud service you choose. On the cloud you can choose between an IaaS, a PaaS or a SaaS.
On an IaaS you will get an infrastructure as a service where you need to install MySQL, the web server, ...
On a PaaS, all these services could be enabled just with click of your mouse and you will just use the service without taking care of the config or the installation process.
This blog article will give you an idea about how to use a MySQL database on a PaaS.
Regarding the web server, for PHP could be something really easy like zip your project and use a command to deploy your application without any config. See here an example.