How to replicate schema changes from local database to a remote?
Next time, click the Generate Scripts button and then execute the generated SQL script at both the local and remote databases.



For the changes you made locally, that you now want to replicate to the remote server, you'll need to either recreate them manually on the remote server or use a tool to identify the differences, such as RedGate's SQL Compare or Visual Studio's Schema Compare tool.

There are other methods, but I think these are likely going to be the easiest approach for you.

Finally, the "proper" way to handle changes like this is to tap into some release management methodologies.  This topic can get pretty complex depending on your needs, but a good primer can be found here along with a listing of some of the tools available on the market.