How can I locate a spider spawner?

You can make a copy of your world then in your copy go in creative mode and use the /locate feature to find an abandoned mineshaft I used this in my single player world an I amazingly found a penta spawner and a quad spawner somewhere else in the mineshaft. I think they are not that rare in mineshafts and if you don't find a good spawner you can go like 500 blocks in another direction and use the locate feature again to try and find another mineshaft.

Take a water bucket with you. It will help a lot to break cobwebs.

If you play solo, you can use an "x-ray" texture pack to see through blocks. It is also helpful if you can install a minimap mod so that when you find a spawner, you can put a waypoint on it and then remove the texture pack.

Also like others said, you can find cave spider spawner easily in a Mineshaft (like picture # 2 of Jim's answer). They always have many cobwebs around, and it's not rare to see 2 spawners near each other.

For regular spider spawners, you must focus on Dungeons (square room with mossy cobble, like the picture 1 of Jim's answer). They have a spider, skeleton or zombie spawner inside.

To make a cave spider farm, make a dark room around the spider spawner then leave a tiny sideways hole (ex. Using glass and fence) to kill them. But don't get too close or the spider may attack you trough the wall.

Try to find a dungeon, which may be located in a cave or abandoned mineshaft. If you don't know what I mean, this is an example:

The dungeon has cobble and mossy stone blocks around it, so it's easy the recognize. It normally has chests of loot. In the middle is the spawner, it's easy to know what it spawns depending on what mob is spinning inside.

If you actually are looking for cave spiders, they're found in abandoned mineshafts. They have wooden fence poles with planks on top, which are easy to recognize, and you'll also find cobwebs too.

If you search abandoned mines, usually spider spawners have a massive amount of cobwebs around the area.

I'm assuming you mean cave spider spawners. The best way to find them is to search abandoned mine shafts. The abandoned mine shafts are generally tunnels 3 blocks high and 3 blocks wide and have wood blocks and fences creating frames around tunnel. They have minecart tracks, cobwebs and random chests placed in them.

Abandoned Mine Shafts - Minecraft Wiki

Also check out What's the best way to find Abandoned Mine Shafts?

Most notably is that you will find areas filled with cobwebs. This area has cave spider spawners. Sometimes you'll find spawners close together but finding 4 in the same area is pretty rare.

Get a mapper, such as minutor, and you will be able to load up your world and easily locate spawners. You will not be able to easily determine their type though as far as I'm aware.

Although slightly outdated, the answers to this question should help too.