Forever adds nine new five-player dungeons for levels 13–60. Nobody has years of muscle memory for them, so a little preparation helps more than usual.
Boss mods
Deadly Boss Mods (DBM) and 
BigWigs Bossmods show timers for upcoming boss abilities and warn you when to move. For a new dungeon they need data for its bosses, written by people who've fought them. Early releases may cover some bosses and not others. Read the changelog: authors usually list the encounters they've added.
Pick one, not both. They do the same job and their warnings overlap.
Party frames
The default party frames are fine for most players. Healers get a lot from something more compact with clear debuff indicators: 
VuhDo and Grid2 have Forever releases, 
Cell doesn't yet. VuhDo has click-casting built in; 
Clique, the standalone click-casting addon, is still waiting for a Forever release.
A meter, for the deaths
Details! Damage Meter tells you what killed someone, in order. In a new dungeon that's how a group learns which ability matters.
Nameplates for tanks and interrupters
Seeing which enemy is casting what is half of dungeon play. Plater Nameplates, 
Kui Nameplates or Threat Plates show cast bars and threat colours more clearly than the default plates.
Without addons
All of this is optional. Read the dungeon journal, watch the boss, and talk to your group. Addons speed up learning; they don't replace it.
Each addon's page shows whether it has a Forever version yet.