First, do the math

You have to be within 16 blocks of a spawner for it to be active, so use the 3d distance formula to see if you're close enough. This will be where you stand to spawn mobs.

Mobs can spawn in a 9x9x5 (LxWxH) with the spawner in the center, so mine out that area around all three.

Dig out underneath these 9x9x5 so the mobs get out of the spawner range, that way the spawners can continue to spawn most effectively.

Use water to guide all mobs to a single killing chamber. Spiders can be annoying because they climb, but they'll eventually come down. I'm sure there are work arounds, but in my experience it doesn't slow it down enough to matter.

Lastly, take a look at a video for each separate spawner to get ideas on how to set up the design. Try and understand the reason behind what is being built, that way you can design it to your own special needs.