"Reeving" a block and tackle sounds nautical and technical, but means nothing more than if you said that you're adding rope to the pulleys--called sheaves--in two blocks. Once the blocks have rope on all of their pulleys, they're said to be "rigged" and the rope between the pulleys is called the "falls." Those ropes are divided into "parts," one on each side of each pulley. Tackle is the "falls" and the block is hooked onto the load you want to move. Each block's bottom is equipped with a pin, called a becket, and a roller called a thimble.
Push the end of the rope through the sheave-opening of one block so, when the block is in use, the rope will rest on the pulley. It makes no difference which block you start with or which pulley you reeve first.
Bring the two blocks together, so the bases of the blocks are touching and their hooks point in opposite directions. Reeve the rope through the sheave on the empty block closest to the sheave already rove.
Reeve the one empty sheave remaining on the first block you rove. Reeve the rope through the only empty sheave left.
Pull the end of the rope to the thimble on the bottom of the first block you rove. Tie the end of the rope around the thimble. Ease the blocks apart, allowing the rope to roll over the sheaves as you do.
The first block you reeve a rope through is always the block to which you secure the final part of the falls. When rigging blocks, the end of the rope should pass under--not over--any previously rigged rope parts. This allows twisted falls to unwrap themselves when the blocks are mounted and raised. If the falls appear twisted, hang the block that you first rove and allow the twist to "hang out" by raising the second block so it is hanging freely. If the twist is still present, turn the lower block upside down, pass it through the falls and release it. This is called "throughfooting the block." A block and tackle with single-sheave blocks is called a gun tackle. With two-sheave blocks, it's called a double purchase. Three-sheave blocks make a threefold purchase.