My main concern with your situation would be that at least for the first 24 hours I would want to be around to keep an eye on it, not that there would be a whole lot that you could do but thats just my preference. Also, you would not want to take it home to your aquarium because you wouldnt want to change its environment immediately before performing the procedure. From what reading I have done the anemone needs to be in a stable environment and very healthy for a minimum of a month for the best possible chances of success. Any change in the anemones environment would put unneeded stress on it.
As pointed out before we would need a proper ID to make sure that it is one that has been successfully propgated before. After that it would be a matter of having a seperate container to do the cutting in, transferring the anemone with water from the tank into the container. Make a cut all the way through the anemone across the disc and directly through the mouth with a very sharp sterile utensil (scalpel or razor). Then you must wait a few minutes because it will secrete mucus that would harm your reef, rinse in another container of tank water, wait a few then place it back into your tank. A few precautions would need to be taken such as decreasing the circulation and making sure the clowns dont pester the anemone. Both sides should wrap themselves to where the freshly cut edges press up against each other and you should end up with two smaller anemone's.
This is just a general description of the procedure from what I have seen, not experienced. I would definitely reccomend that you read alot on this subject and get as much advise as you can from those who have actually done it.
