How do i shutdown my heroku app?

To stop a DYNO you can use:

heroku ps:stop "appname"

To get list of running appnames you can use:

heroku apps

Just read the documentation:
https://devcenter.heroku.com/articles/one-off-dynos#one-off-dynos

Type

heroku ps

to see all running app associated to you account, with an id associated, then

heroku ps:stop run.1

if the app you want to stop has the 1 id.

Note that the maintenance mode will not stop your app. Mine was wrongly configured and continued to crash with the maintenance mode enabled.

From web: Personal => Your App Name => Overview => Configure Dynos => Click on edit against web => Flip the switch => Confirm

To shut down your Heroku app scale the web processes to 0:

heroku ps:scale web=0

See the Usage & Billing dev centre article: "A web dyno that is idled continues to accrue usage". I believe maintenance mode will continue to accrue time; it simply serves a static page to visitors instead of serving your app.

Keep in mind each app receives 750 free billing hours per month. Depending on your intended usage, this may mean you don't need to shut down (i.e. if you only plan to run a single dyno for the whole month).