Minecraft – How to make a treehouse that spiders can’t get into

There is no way to guarantee mob spawns of a particular type unless you happen to find a mob spawner. Your best bet is to simply set up a situation that allows a lot of enemies to spawn and then weed out the spiders.

There are a variety of traps that can be set up, from very simple to very complex. One of the easiest ways to get a lot of enemies to spawn, however, is to simply set up a tower in an open area (keeping you safe and able to see a large distance).

Spiders have three attributes that you can abuse to catch them:

• They are 2 blocks wide by 1 block high. All other enemies are taller than they are wide, so a 2x1 hole will allow spiders through while keeping you safe from other enemies. This can allow you to deal with them specifically if you want to build some sort of trap room.
• Spiders do not die from sunlight. This is why the tower tends to work well - even if a lot of monsters spawn nearby, you can wait for sunrise and then you will only have to watch out for creepers while you take down whatever spiders have spawned. As an added bonus, spiders will not be hostile during the day until you attack (or if they were already after you from nighttime).
• Spiders can climb walls (but a lip will stop them). A platform, at least two blocks high and well lit, can help you separate the spiders from other monsters, as only they will be able to climb up after you.

I always put my lip just high enough so that I don't bump my head on it (that is, with 2 blocks of air between the ground and the lip). I have watched it stop spiders and have never encountered a spider above the lip. James' answer is correct about the spider AI.