Rinse it off under the tap or in a bucket of water if you have one big enough.
Just a caution, spider wood is known to sometimes contain a toxic fungus that will kill fish. I had this, as have others. Some fungus is safe for fish, some is deadly, and there isno way to tell without an examination by a qualified microbiologist. So if you see any white slime/fungus, it might be best to discard the wood.