UP HERE IN CENTRAL NEW YORK WE HAVE A SHORTER GROWING SEASON THEN WHERE SWEET POTATOS PRODUCE ABUNDANTLY.  SWEET POTATOS NEED FULL SUN AND HEAT.  I HAVE TO START MY SLIPS AROUND MID FEBRUARY. 
YOU WILL NEED A  FIRM, HEALTHY SWEET POTATO.  MAKE SURE THE EYES ARE NOT DAMAGED.  IF YOU BUY THEM FROM THE GROCERY STORE THEY MAY BE TREATED NOT TO SPROUT.
FIND A CONTAINER THAT WILL FIT YOUR TATER.  IT NEEDS TO BE SUBMERGED HALFWAY IN WATER, POINTED END UP.
I USE TOOTHPICKS STUCK IN HALFWAY UP THE TATER AND REST IT ON THE SIDES OF A QUART JAR.
KEEP WATER LEVEL AT HALFWAY MARK.  CHANGE WATER EVERY COUPLE OF DAYS.
IT DOESN'T HURT THE SWEET POTATO TO REST IT ON THE BOTTOM OF THE CONTAINER.
KEEP THE SWEET POTATO IN A WARM PLACE.  THEY NEED WARMTH TO SPROUT.  I KEEP THEM IN MY KITCHEN WINDOW SILL. 
DEPENDING ON THE TATER AND THE HEAT.  THEY SHOULD SPROUT WITHIN A COUPLE OF WEEKS.
I LET THEM GROW UNTIL THEY ARE ABOUT 6" LONG. 
SNAP THE NEW SPROUTS OFF THE TATER AND PULL THE BOTTOM LEAVES OFF.  PLACE THEM IN ANOTHER CONTAINER OF WATER AND THEY WILL GROW ROOTS WITHIN A WEEK. 
PLANT THEM IN POTS WITH POTTING MIX(OR DIRECTLY INTO THE GROUND, DEPENDING ON WHAT ZONE YOU LIVE IN)
I USE THE PEAT POTS, SO I DON'T DISTURB THERE ROOTS WHEN I PLANT THEM.  I CRACK THE POTS OPEN AND PLANT.
HERE, I DON'T PLANT MY SWEET POTATOS UNTIL A WEEK OR SO AFTER OUR FROST FREE DATE(MAY 31ST).  DEPENDING ON THE NIGHT TEMPERATURES.