In case of Java and Selenium. We check in our code into client's repository. Usually Git repository or SVN repository. And also we set up CI servers like Jenkins or Bamboo for them. So on daily basis, whatever our test automation engineers create/write/automate will be added to the client's repository. From there the CI like Jenkins or Bamboo will get the code and compile it and execute it.
Most of the time, we use Maven or Ant based Java project. So, we just have to create Maven build. After build is executed. The report will be zipped using CI and mailed to the client and stakeholders.
In case of Specflow or SpecRun, you can use Jenkins CI and execute your DLL files as command lines. The same way you execute those on your local machine.
You will need DLLs and all supporting files to be setup on CI server for execution. Make sure that it generate reports and logs which can be emailed.
You can even try exploring TFS(Team Foundation Server).
Hope that helps!
