Drill a one- to two-inch wide hole in existing concrete using a high speed electric drill with a masonry bit. Clean out the inside of the hole and around the hole with a fiber brush.
Mix the concrete with water and fill the hole to within two inches of the top.
Center an anchor bolt in the hole to a minimum of a four-inch depth. Let the anchor bolt extend at least one inch above the top of the hole if you are anchoring a flat plate, more if you are anchoring an object of any depth.
Fill in the remainder of the hole with concrete and smooth it out with a small metal trowel, leveling it around the anchor bolt. Smooth and level the new concrete to the existing concrete. Let the concrete set for 24 hours.
Drill a hole a little wider than the anchor bolt in the material you are fastening, using a metal or wood bit (depending on the material you are anchoring). Slip the anchor bolt through the object so that the anchor bolt protrudes. Attach the washer and nut to the top of the anchor by hand, then tighten it with a wrench or other appropriate hand or power tool.