Firstly, when you say "theme" I am assuming you mean a set of templates.
There are a few ways to approach this.
Copy your entire local installation to the remote server
If you have the site working on your local machine and simply want to now put it on a remote server then you do not need to run the installer on the server. You can copy the files to your server via FTP then create a backup of your local database and use this to recreate a database that your remote site can connect to.
The problem then, however, is that you will need to update any paths used to make them work on the remote server. This can be done manually but is a bit fiddly or you can look at something like Deeploy Helper or Reelocate which will let you update all the paths used in one place.
My preferred option is to use Focus Labs Config which will allow you to create different configs to be used in different environments.
or, Install a fresh copy of EE and update parts of it
This is the approach you are partly taking already. Basically create a completely clean installation of EE on your remote server, complete with a fresh database, then replace some of the files and upload a copy of your database.
Once you have a fresh installation on the remote server:
Back up your local database to an SQL file and use that file to
overwrite the freshly installed remote database.
Then copy your templates directory to overwrite the one on the
If you have any third party add-ons installed then you should also
copy the /system/expressionengine/third-party and /themes
directories to your remote server.
Copy your local images directory to the remote server as well as any upload directories you have created.
Update the config file on the remote server to reflect the new environment
You will also need to update paths and set permissions for config files, templates, cache, and file upload directories to reflect the new environment