You should get some hydrochloric acid as well. Preferably, high concentration. Hardware stores have 10 M HCl. The H2O2 should be high conc as well, but 3% will work just fine.
1. Make a saturated solution of KI. Warm up the water for maximum KI.
2. Add HCl. I think some KCl will precipitate.
3. Add the H2O2 and the solution will turn dark.
4. Decant and wash the iodine.
5. If you want, heat the liquid and distill off the iodine that is dissolved in the water.
The reaction is
KI(aq) + HCl(aq) -> KCl(aq) + HI(aq)
2 HI(aq) + H2O2 -> I2(s) + 2 H2O (iodide gets reduced, H2O2 gets oxidized)