How to run programs from an external hard drive on MacBook Pro?

I need to know how to install and run applications from an external hard drive on my MacBook Pro.

You just need to copy the application to the external drive. Mac apps can actually run from anywhere, it is merely convention to keep them in the /Applications folder.

Of course all the preferences will still be in your home Library folder but the app will be on the external drive.

It is possible (with conditions). You need to take care of:

1. The external drive must be formatted in some Apple/Mac Filesystem like HFS+ or APFS. If you try to run those external apps from an exFAT or some other non-Apple/non-Mac file system, macOS will complain about a "corrupt or broken" app, even though the app itself would be totally fine.

2. Be careful when the apps on the external drive want to self-update. Those updates may or may not land in the Application folder on the main mac drive (and not the external drive).

3. Unlike the .apps applications which you can just drag and drop out of your Applications folder onto an external drive, some apps have installers instead (e.g. often the ones where the setup comes with .pkg extensions, and NOT .dmg extensions). Those often want to install themselves on the disk where the macOS itself also resides (e.g. Labview, MacTeX, R).

4. Some apps, even though they may say that they have an "installation path" option (e.g. Microsoft Visual Studio), they still install 90% of their stuff onto the main drive where macOS resides. So you earn next to nothing from using an external drive for such apps.

The following are not deal breakers and are self-obvious but just to be complete:

1. Speed could be an issue, in general. Some apps might behave sloppy.

2. You can use the apps only as long as you have the external drive. (Convenience factor?)

3. For some apps, even on an HFS+/APFS formatted disk, the macos throws an error that the app cannot be verified. You can still go to the Settings->Security/Privacy->General and launch the app anyway though. Depends on how you feel about that viz-e-viz security, app-verification, etc.

4. Macbooks (especially the newer models) have fewer ports (USB, SDCard, etc). I have not tested it (cause thankfully my macbook is old and hence has enough ports), but I can imagine that the performance of an external drive connected to a shared USB port over an external Dongle or USB hub would suffer when other USB devices also want a piece of the action with the macbook, over that USB port.

p.s. like the Answer from Tony mentions, this all affects only the executables. The preferences, etc don't get moved (with exceptions again! I noticed the Tor Browser puts its data right there on the external drive. But then again Tor Browser is aiming for something else than most other apps).

Last word: For convenience' sake, one can even make links to the external apps from the Applications folder, like so:

$ cd /Applications
$ ln -s /Volumes/<EXTERNAL DRIVE NAME>/dosbox.app dosbox.app

and henceforth you can launch those apps from the Launchpad.