The size of the tuber depends on the variety of the lily.

The size of the tuber is mostly related to the size of the plant.  Large spreading lilies have larger tubers.  Smaller sized lilies have smaller tubers. Look at the photos below.

Lilies are shipped bare root because they do not travel well with leaves. So for this reason we remove all large leaves for shipping.  It is no big deal really because each lily pad only lives a few weeks before it turns yellow then brown and dies.  Lilies are constantly sending up new leaves all the time.  These new leaves  replace the leaves that have died.

Once you open the box with the lilies if you can not plant right away put the tuber in a bucket of water.  If you have city water be sure to add dechlor.   The tuber will keep for a week or more.  Change the water out of the pot if it the water becomes nasty or smelly.

For hardy lilies do not put them in your pond unless the water is at least 55 degrees.  For tropical lilies the water must be at least 70 degrees.
 

Then cover with dirt.  Then top with gravel.  Make sure the gravel comes up to the crown (the crown is where the leaves emerge on the tuber.  Do not cover the crown!

Fill a 5-gallon bucket and slowly drop the pot into the bucket so that you do not wash the soil away.  Leave the plant sit for few hours.  By doing this the loose dirt will go in the 5- gallon bucket and not your pond.

After a couple of hours remove the potted lily and slowly lower it into your pond.  Take your time so that you do not get the dirt in the water.

Many buy plastic dish pans in the dollar stores and use them for lilies.  They work great and you generally do not have to re-pot but every other year.

You want to use at least a 1-gallon  black nursery pot, bigger is better in the pot size.  For my personal lilies I generally use a 3 to 5 gallon sized pot.

In a few days if your water is at least 55 degrees you will see the leaves enlarge and work their way to the surface.

Hardy lilies can go as shallow as 6 inches or as deep at  24 inches.

If you have to buy dirt look for bags of topsoil.  It should feel heavy in weight.  DO NOT use potting soil.  It is too light and is sometime contains perilite (looks like small pieces of Styrofoam) because it will just float out of the pot.

The dirt you use should contain clay to hold together.

If your water is at least 55degrees you will see lots of leaves as the water gets warmer.  Generally speaking lilies will start blooming a few weeks after planting.  But a lot depends on the water temperature.

These plant stands are great if your pond does not have plant shelves or your water is deep and you need to raise the pot off the bottom of the pond. They come in two different sizes.  All steel constructed.  Powder coated for rust resistance. Assembly is required.  Stands are not assembled to save on shipping box size.  

Both sizes are adjustable from 18" to 22" tall.   Shipping weight on 1 is 5-1/2 pounds and the shipping weight on 2 is 11 pounds. I can only ship 2 in the same box. Large quantity is available if I can find a big enough box.

Size 1 holds pots up to 12" in diameter 
Size 2 holds pots up to 16" in diameter 

Click photos to enlarge.