Wait until fall when the foliage has yellowed, then dig up the clump and carefully separate the bulbs and replant them .

Since it's best done during the cool fall weather you can mark your calendar now and learn a bit while you wait.

I like how detailed B&D Lilies.com explains how to transplant including what to do with the shovel & your hands. It's almost like someone is showing you how to do it & I learn best by doing.

"When all leaves have turned golden yellow or brown, cut stems down to 5 or 6 inches above ground level before starting work. Set your spading fork or shovel 4 to 6 inches away from the outer stem of a clump and dig down one complete shovel depth, at least 12 inches. Gently work your way around and under the white, pink or purple colored bulbs to easily lift them out of the ground. Bulbs which have put up multiple stems have either divided or produced smaller offshoots called bulblets. Gently tease them apart from each other, sorting as you go. Work with only one variety at a time to keep from mixing up different named clones.

With your fingers, clean excess soil from the bottom and sides of larger bulbs. There will be a group of stem roots just above the bulb that may have a few bulblets hidden within the cluster; you can use a garden hose to wash off soil to make them easier to find if you would like to save them, but any washed bulbs will need to be "air dried" for an hour or so before planting. Cut the old stem just above the large bulb and discard; stem roots are feeding roots, they grow new each year and are not needed over winter. Any bulblets that might be attached to the old stem can be gently removed at this time.

Plant larger sized bulbs with 4 to 6 inches of soil covering the top of the bulb, smaller ones or bulblets more shallow into already prepared soil. Dianna always recommends that you dig the receiving holes first, then dig out the bulbs for transplanting. Lilies do not like to dry out and an overzealous individual may tire or run out of time to finish the job in the same day, a good plan for moving other plants also, so don't take on more than you can completely do at one time.

Our lily bulbs that are dug in winter, and stored for spring shipping, are carefully packed in large bulb crates with attention given to proper moisture levels, moved to coolers in late November and the temperature is then slowly dropped to mimic a natural winter. This is difficult to achieve in a home refrigerator, the reason why lilies need to remain planted in the garden and not "stored" bare in a shed, garage or fridge over winter."

You can find more info on their website.

Here is a link that might be useful: photos on how to divide lilies

I don't take the instructions from B&D too solemnly. They are written as for small children and maybe some readers need it this way. Lilies are not hand granades. The vulnerability of lilies to drying up is greatly exaggerated. I had a bucket of forgotten lilies in my dry basement through the whole winter (wiht some soil). I planted them out in the spring and many of them still sprouted. So do not dispair just because they lay some days in the shade. I replant them 3-4 weeks after blooming time. Majority of Asiatics are ripe to be replanted. They will not grow much(if at all) even if the leaves are green. It is better for them to develop better root system before the winter, than to have 1 mm more in diameter.

I agree with hostaholic 2 with one more suggestion. Before you dig, cut the stems to about 6 inches. Then when you replant the soil line on the stem will serve as an indicater as to how deep to replant. Also, do not try to remove this short stem as this may cause bulb damage affecting next years growth. And, since lilies don't always grow staight up from the bulb, when you dig--start back about 6 to 8 inches. Water in real good once. Being fragrant and large pink star shape, you most likely have a hybred oriental so if you're live in the northern states-say zone 5-you should mulch them after the ground freezes. Good Luck!