Question
I have recently bough princess lillies and the blooms are gone. Do I need to prune these flowers and if so how?

Answer
These are also called Dwarf Alstroemeria.  As with all flowering plants, you would be doing your plants a favor if you would remove all the spent, finished flowers before they start expending huge sums of energy in seed production, which is what they do as soon as possible once flowering is finished.  Cut off the finished flowers with a scissors or by hand, but remove them asap to avoid this useless seed-making exercise.  The plants will be much healthier if you do that.

That's the only pruning you should worry about for this plant.

Cornell University Cooperative Extension warns that 'Alstroemeria cultivars are not often hardy in the colder zones' but I don't know if this is going to be a problem for you as you did not identify your location on Planet Earth therefore I don't know if you are in Juneau Alaska or Oshkosh Oklahoma or the Island of Fiji.  See the Cornell notes here:

aggiehorticulture.tamu.edu/ornamentals/Cornell_Herbaceous/plant_pages/Alstroemeria.html

Your compact Princess version of Alstroemeria was the product of 'meticulous work focusing on smaller size and an abundance of flowers'.   All care and feeding is detailed at the Easy to Grow Bulbs.com website:

http://www.easytogrowbulbs.com/index.asp?PageAction=VIEWCATS&Category=198

Note that this plant is evergreen only in 'mild' climates.  If you are looking out the window at palm trees right now, it will surely continue to thrive in your region.  If you are looking at fir trees, you are in trouble.  Regardless, these are beautiful, beautiful flowers, and you are very lucky to have them.  Thanks for writing.

THE LONG ISLAND GARDENER