After publishing for the first time you will need to start Solr. This is done in command prompt. Navigate to the published site, then /solr/bin folder and running solr start -p 8983. The output will let you know Solr has started on port 8983.

You will be able to access Solr externally for testing at https://server_name:8983.
To stop Solr in command prompt by navigating to the /bin folder and running solr stop -p 8983.
Solr should be registered as a windows service in order to keep solr running after you log off the server.
We use a tool called NSSM that allows us to run .cmd as a service on the server.
Downloads NSSM prelease build 2.24-101, or the correct version for your server. Unzip the file and add the 64 or 32 folder to your system path.
After adding NSSM to your path you can add a service by
nssm install atlas-search
Add the path to your Atlas install. Add in the start up params. Be sure to include the -f flag to run solr in the foreground. This will let windows services cleanly stop/restart the service.

Finally, you can start the service from the windows services manager.

The nssm service can easily be edited with nssm edit atlas-search.
When publishing the website again, you may need to stop solr before publishing.