Drill into the mortar in between the bricks with a rotary hammer drill. When anchoring to a brick or cinder block wall, the mortar is stronger than the brick.
Drop a few drops of water on the drill bit while drilling. The water keeps the bit cool, and helps dissolve the mortar as you drill.
Insert the wall anchor, either plastic for smaller fasteners, or metal masonry anchors for larger fasteners, into the hole. Make sure the hole is drilled deep enough for the anchor to sit flush with the surface of the wall.
Insert the appropriate fastener, and tighten the fastener. Do not over tighten the fastener. Masonry anchors have a tendency to strip out if they are over tightened.
Drill a hole all the way through the brick wall when you do not have the ability to drill into a mortar joint, or when you are mounting a heavy object to the wall. Each masonry anchor is rated regarding how much weight it can hold. If your project exceeds the manufacturer's recommendations, plan on bolting though the wall.
Drill through the wood that is behind the brick veneer. Brick is installed over the surface of a wood framed wall. Make sure to drill all the way through both.
Insert a threaded rod through the wall, and into the wall cavity on the other side of the brick. Go around to the other side of the wall, and thread a nut and washer on the threaded rod. This fastener will spread the weight across the entire wall area.
Return to the front side of the wall. Screw another nut and washer onto the front side of the threaded rod. Now anything you bolt to the brick, or fasten to the threaded rod, is supported by the entire wall.