Best Practices

Assuming that you're talking about one database and identical tables(some people connect to a 2nd database), you'll find your MySQL connect information in dbcommon.php. You will need to copy & keep a separate dbcommon and upload it to the internet. This one will have the information required to connect to your database on the net. You will find dbcommon.php in the include directory.
$host="localhost";

$user="userid";

$pwd="password";

$port="";

$sys_dbname="database name";
Once this is set up, then you will be ok.
Al

Al,
in PHPRunner 5.3 you don't need to modify dbcommon.php manually. You can setup several connection settings on 'Output directory' screen.
Ofi,
PHPRunner doesn't synchronize tables and data. You can either develop your application connecting directly to remote server or use a third party software to synchronize local and remote databases.

I hadn't notice the addition. Nice new feature.
Al

Do I need to create two server database connections for my scenario where I have a local DB and a remote DB?

No. You don't need to set up server database connections for local db.

Server database connections is used to point files on the web server to the database since connection details are different on your local machine and on the web server.

OK, it is still unclear to me how to work with two databases (one local and one remote) through PHPR.
If I develop locally, what should I do to synchronize the remote database to look like my local version?
I can see how it could be done via phpMyAdmin with export and import, but is PHPR capable of doing this instead?

PHPRunner does not synchronize databases. There are excellent third party tools that can do the job. PHPRunner is about building the code.
Both Navicat and SQLYog can synchronize MySQL databases:

http://stackoverflow.com/questions/52583/best-tool-for-synchronizing-mysql-databases

So the procedure is to develop locally, upload the code with "Publish via FTP" and sync the database structure manually. Is that correct?

It really depends on many factors. If you plan to modify database structure a lot - develop everything locally, test it, then upload everything to the server and synchronize databases. This approach makes sense if you already have a live application you cannot afford to break.
If you just starting you can connect directly to database on the server and make changes there. This going to save you synchronization step though it's going to be a bit slower (remote connection are always slower) and a bit riskier.
On the long run first approach is preferred.

Understood. Thanks for the advice.