As far as I understand you have your project on a development server, test server and on a production server. After you make some changes in the project for example on the development server you would like to move these changes to the production server.
If so, you can use our Site Synchronization module in order to synchronize any type of content between different environments as it is described in this article
from the Sitefinity documentation. You can also check this video
on how to work with the Sitefinity SiteSync module.
If the Site Sync tool is not an option for you, the best way to move the changes from the development to the production server is to copy the project and the database from the development to the production server and then fix the connection string to point to the database on the production server.
Regarding the custom module, if you have created the module using Module Builder in your development environment, you can export the structure of the dynamic module and the import it in your production environment. Please refer to the following article
for more details about this.
Do you want to have your say in the Sitefinity development roadmap? Do you want to know when a feature you requested is added or when a bug fixed? Explore the Telerik Sitefinity CMS Ideas&Feedback Portal
and vote to affect the priority of the items