I have Bitcoin-qt installed and running on an external Hard Drive. Where should I put the bitcoin.conf file so I can configure it with the server setting, user, and password?
It depends on what OS you've got. Windows, Linux, Mac OS?
That said, one of the many possible solutions is somehow OS-independent: move everything to one single directory on your external disk including the wallet.dat file, the .conf file, the executable, and the blockchain data. Then make sure you always start your Bitcoin-Qt client from the console and include the parameters -datadir and -conf in your command line. Here is an example for Linux:
cd /my_external_harddisk/bitcoin/ ./Bitcoin-Qt -datadir=. -conf=./bitcoin.conf -printtoconsole
(I added the optional -printtoconsole parameter. This prevents inflating the debug.log file somewhere on your OS disk all the time.)
In MS-Windows it would look very similar, I guess (I haven't got access to a Windows PC at the moment).
In Mac OS you may want to keep everything in a directory containing Bitcoin-Qt.app for practical reasons, but the principle is the same:
cd /Volumes/my_external_harddisk/bitcoin/ Bitcoin-Qt.app/Contents/MacOS/Bitcoin-Qt -datadir=. -conf=./bitcoin.conf -printtoconsole
If you later inadvertently start Bitcoin-Qt without any parameters then it simply creates an empty wallet.dat file in Bitcoin's standard directory somewhere on the OS disk. At first glance this looks as if you suddenly lost all your precious Bitcoins. Don't worry, your original wallet.dat file is still there on your external HD in perfect condition. Just exit the program and restart from the console with the parameters as explained above.