Cinder block is a difficult medium to attach anything significant to; its porous, baked-hard surface that tends to break away when drilled. One fastener for the job is an epoxy bolt, manufactured for use in cement and with epoxy glue. An epoxy bolt is a threaded shank that comes with a nut. It's generally regarded the strongest masonry anchor. Read the manufacturer's specifications for proper and secure installation.
Measure the wood and cinder block to determine the exact location you intend to join the two together. Mark the block with a marker.
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Use a masonry drill bit to bore into the cinder block. Read the manufacturer's information for the proper bit size and hole depth. Mark the drill bit at the necessary boring depth to avoid drilling too deep. Most of a cinder block's surface is 1 inch thick and can accommodate an epoxy bolt three-quarters of an inch deep. Strategic places on the top, middle and bottom ends of the cinder block are thick enough to accommodate longer bolts.
Clean out the hole with a stiff wire brush, taking care to remove all loose debris. Avoid being too aggressive and causing the hole to enlarge from the friction of the brush. Repeat until all the loose concrete is gone.
Blow compressed air from a canister or air compressor into the hole to remove leftover dust from drilling and brushing.
Apply epoxy cement from a dual applicator tube, which mixes the two agents in the right ratio for maximum strength. Apply epoxy until the hole is halfway full. Start at the deep end of the hole and work outward.
Insert the epoxy bolt into the hole and twist it clockwise several times until it is covered in epoxy.
Clean off any epoxy that has gotten between the nut and the surface of the cinder block. Clean the threads with a clean rag if necessary.
Twist the nut on the anchor bolt, moving it down to the surface of the cinder block. Allow the epoxy to dry thoroughly before securing anything to the bolt.
The length of the exposed threaded end of the bolt, plus the size of the nut and a washer, will determine the thickness of the wood that you can attach to the block. Place the washer between the nut and the wood, and the wood secure with a wrench or socket tool until snug. For some applications, brackets make attachment more viable: Secure the wood to the bracket, then secure the bracket to the epoxy bolt on the cinder block.