Before anything - keep in mind that this only applies for Campaigns that are using the Lead Generation objective. For Conversion Campaigns using the Lead Generation conversion event, this will not apply.
Simply select the campaign(s) for which you want to download your leads and refer to the action bar at the top of your screen:
If there are several lead forms, you will see a screen offering each of them, asking you to select the one you wish to download:
If you only have one, it'll download instantly!