How to cheaply extract iodine from an alcoholic solution?
Alcoholic solution of iodine

What firstly comes to mind is that you meant &quot;iodine tincture&quot;.
This question must have been frequently asked, since answers are available out there with different degrees of reliability. You must first follow the safety instructions:

Do your experiment somewhere that the noxious fumes won't be able to do harm to anyone. It's best to work under a fume hood.
You're gonna be dealing with strong acids. They're very corrosive when in contact with skin, metals or anything you can imagine (except glass).
Iodine tends to sublime. If not contained wisely, you'll get irritated skin, along with damages to your eyes (See about iodine hazards here).

In short, what you should do is:

Pour the tincture in a beaker, or any container. The important thing to note is to have &quot;control&quot; over what's happening in there.
Add water to the solution. The volume of the water you add should preferably be equal to that of tincture.
Add $\ce{HCl}$ to the solution, $\approx \pu{5-7 ml}$.
Add bleach to the solution, preferably equal or more than that amount of $\ce{HCl}$ you added.
Wait...wait...wait. For a relative amount of time, you should leave the solution for the reactions to happen.
You've past the hard part! Congratulations! Now, filter the dilute solution with a coffee filter.

Additional tips:

Iodine crystals sublime, so you shouldn't leave them in open air for long.
You should at least be wearing appropriate eye and skin protection. If you don't want them, do not do the experiment!

Wikihow has additional tips in case of any failures.
Sources:
http://www.wikihow.com/Extract-Iodine
http://www.sci-spot.com/Chemistry/iodine.htm