I just came across my first dungeon in Minecraft, and already the Mob Spawner is giving me problems. What would be a quick way to destroy the Spawner? All the Minecraft wiki mentioned was ways to trap mobs.
To break one, use a pickaxe, preferably Iron level or higher. Note, once you destroy one, it will not drop as a block, so break these only if you'd like to get rid of them permanently.
While your opinion may differ, I find spawners to be excellent exp farms, and you can turn yours into a mob farm.
If you'd rather save your Mob Spawner, you need to block it off with light, similar to placing torches in a cave to ward off mob spawns. To de-activate a mob spawner, place torches around the spawner (at least an 8 block radius) to prevent mobs from spawning. Put them adjacent to the block itself.
If you want to destroy a mob spawner quickly, you want to place torches close to the spawner and destroy it after killing the remaining mobs around you to stop them from slowing you down. This method differs between different spawners. Cave spider spawners are difficult to get rid of for a begginer. You should destroy the webs from a distance and place torches frequently to prevent the spawn rate and eventually stop them spawning. Cane spiders spawn quite quickly and do give decent xp. This may encourage you to make a mod trap.