Minecraft wiki entry for Nether_survival, associated text: For your first fight, kill blazes that are not in the spawner room. This lesser number of blazes are easier to fight when you don't have a potion of fire resistance.
If you haven't brought out the enchanted armor, now's the time. Fire Protection and Protection are both helpful.
An enchanted golden apple is good to bring, but if you haven't acquired one yet potions can act as a substitute. Specifically, potions of fire resistance, strength, and regeneration can be a huge help. Although Potions of Fire Resistance make you immune to blaze fireballs, you are not immune to their touch attack. Armor and regeneration potions can help.
An iron golem may be helpful, especially once you've got the spawner contained. One big disadvantage is the golem's huge knockback, which can throw Blazes and their drops out of reach. The golem's distractibility is also an issue — between spawnings, they're liable to wander off after zombified piglins and wither skeletons. The zombified piglins don't mob you or the golem for the golem's attacks, but the repeated fights soon wear down the golem. (A splash potion of regeneration or repairing the iron golem with iron ingots can help with that)
A creative option is to mine under their platform to make a bolthole with a narrow opening up to their platform, perhaps 1×3. As they descend into the hole to reach you, you'll be able to get in several hits before they can respond. Nether fortress stairways (the narrow sort, not like the one leading to the Blazes) can provide a similar bolthole.
A fishing rod can be useful for pulling blazes into melee range so their drops aren't lost.
Create a "ceiling" above the spawner-this prevents blazes from flying out of reach and makes it easier to obtain their rods.
It takes 7 snowballs to kill a Blaze. Water can't be used in the Nether, as it simply fizzes and vanishes. You can try making a Snow Golem, but they'll quickly "melt" due to the Nether heat. (Again, splash potions of fire resistance can help.)
With fire resistance assured, you may want to seal yourself in the spawner room, so that wither skeletons, magma cubes, or other Blazes can't ambush you from behind.
Bring a shield to block the fireballs.