First you need to navigate to the Search tab and then search for the competition that you want to set notifications for.

You then need to press on the name of the competition which will take you to that competitions page. 

One of the options on the competitions page is 'Notifications,' press on that and then you can select which notifications you want to set.

On Android you can set 'default notifications' (more info about them here) or 'custom notifications' where you can use toggles to choose which notifications you want.

On iOS you can only choose from custom notifications and can use the on screen toggles to choose which notifications you recieve.

Here is a video showing how to subscribe to notifications for a specific competition: