The simplest of the Persian weaves family. Many people find this weave hard to start out. I suggest pinning the rings down on a piece of styrofoam until you have the weave down pat. Many people keep 'tails' of the weave, as it is easier to build off a started chain, then to begin a new one.

The White rings are the newly added rings, The orange rings are ring(s) in which the New ring passes through. The Green rings are rings already added to the chain.

Step 1: Close three rings.

Step 2: Pass a new ring through these 3 closed rings exactly(if not, the weave will not work correctly) then close the added ring.

Step 3: Lay another closed ring underneath the end of the chain, like so:

Step 4: Add another ring through the middle of the last 2 rings on the chain, and through the newly placed closed ring, like so:

Step 5: Add another closed ring underneath the end of the chain.

Step 6: Add another ring through the middle of the last 2 rings on the chain, and through the newly placed closed ring, like so:

Step 7: Reapeat steps 5 and 6 until desired length.
Backside
Frontside

Thanks to Eli for the Generated Pictures!