I have hosted Sitecore on Azure platform using Sitecore Web Experience Manager 8.2.
How to sync Content delivery server and content management server, so I can push my files and changes to content delivery server?
Based on the question, I will take a stab at the answer as a 'Sitecore fundamentals' approach, rather than digging into the weeds too deep.
Sitecore's Content Management and Content Delivery server are both instances of Sitecore which connect to a set of databases that store content and configurations. When you publish in Sitecore, what you are really doing is copying data from the one database ('master') to another database ('web'). The Content Delivery server is typically configured by default to serve up a default website pointed at the 'web' database. By doing this 'publish' you make the edits you make to content show up on the Content Delivery server.
Often, you also have content changes you will make (custom templates, rendering definitions, etc.) that will need to be deployed to your database as well. You will store these in your development solution in some way so you can track what changes you made to Sitecore databases. These also need to be deployed.
There are several tools available that you can use, but Sitecore is currently promoting the use of MSDeploy packages for deploying to Azure. DACPAC can be used for database changes and your files go in as usual for an MSDeploy package.