In order to use a Remote Raid Pass, the raid must show up in your "Nearby" tracker. The range is not infinite, remote raid passes will not let you see raids you couldn't see otherwise.
Under the icon for the raid in the Nearby tracker, a small "View" button will be visible that will take you to the gym, similar to when you click on a defender pokemon to visit the gym it is in. Once at the gym, the "BATTLE" button will be purple and say
using a Remote Raid Pass
Click the button and it will put you in the lobby.
EDIT: A feature to invite in-game friends has been added. Once in a lobby there is a small button with an icon that looks like "plus person." If you click on this, it will let you send an invite to anyone on your friends list. They will receive the invitation in their nearby raids tracker. If they click on that invitation, they will be brought to the gym and allowed to use a remote raid pass to join the lobby. Be aware that the invite only lasts until the lobby runs out of time, so if you send invites with only a short time left your friends may not see it and react before the fight starts, locking them out of the lobby.