All these answers are obsolete now.

Currently you have to:

1. install the Python language extension (and Python, obviously)
2. open folder (important!), open any Python file inside that folder
3. switch to debug "tab"(?) and click on the gearbox (with hint 'Configure of Fix 'launch.json'')
4. save the opened launch.json file (it's placed in .vscode subdirectory in the folder opened in step #2)
5. finally, click the green triangle or hit F5

No additional extensions or manual launch.json editing is required now.

This worked for me:

.vscode/settings.json:

{
    "python.linting.pylintEnabled": false,
    "python.pythonPath": "python.exe"
} 

.vscode/tasks.json:

{
    "version": "2.0.0"
}

.vscode/launch.json:

{
    "version": "2.0.0",
    "configurations": [
        {
            "name": "Python",
            "type": "python",
            "request": "launch",
            "stopOnEntry": false,
            "pythonPath": "${config:python.pythonPath}",
            "program": "${file}",
            "cwd": "${workspaceRoot}",
            "console": "internalConsole",
            "debugOptions": [
                "WaitOnAbnormalExit",
                "WaitOnNormalExit",
                "RedirectOutput"
            ]
        }    
    ]
} 

You can replace "program": "${file}", with "program": "${workspaceRoot}/main.py", to run your main file no matter which file you've selected but I found that that makes errors like syntax errors sometimes not display correctly if at all.

Breaking on exceptions

1. Press CTRL + SHIFT + D
2. In the BREAKPOINTS panel, click on Uncaught Exceptions enter image description here