Spells and abilities that would normally cause you to gain or lose life still resolve while your life total can't change, but the life-gain or life-loss part simply has no effect.

If a cost would include causing you to gain life, that cost can't be paid. Similarly, you can't pay a cost that includes the payment of any amount of life other than 0 life. However, you can choose to be dealt damage, even though that damage won't result in your life total changing.

The effect of Flare of Fortitude doesn't prevent damage. Rather, it changes the results of that damage. For example, if a creature with lifelink deals damage to you, you won't lose any life, but its controller will still gain that much life. Similarly, if a creature you control with lifelink deals damage to another player, that player will lose life but you won't gain any life.

Abilities that trigger whenever damage is dealt to you will still trigger because that damage is still dealt, even though your life total doesn't change as a result.

Effects that would replace having you gain life with some other event won't be able to be applied because it's impossible for you to gain life.

Effects that replace an event with having you gain life (like Words of Worship's effect does) or having you lose life will end up replacing the event with nothing.

If an effect says to set your life total to a certain number, that part of the effect won't do anything.

If an effect would cause you to exchange life totals with another player, the exchange won't happen. Neither player's life total changes.

In a Commander game, the damage dealt to you by commanders will still be counted, even if that damage doesn't cause you to lose life.