Deadhead the spent flower. E.g. cut the small pedicel (miniature stalk which holds the flower to the stem) off but let the main flower stem (with leaves) stay. This flower stem is needed to conduct photosynthesis and recharge the plant for next year.

Fertilize now if you have not already done so.

I am sorry that I don't have a picture with spent flowers, so I used a lilly in full bloom. Obviously you should not cut flowers/buds off before they mature (wither and die), but the picture below will show you where to cut approximately.

I know what you mean by that minature stalk, I was wondering what to do about it.

Very helpful info, thanks so much!

Will my lillies bloom again this season? Do lillies only bloom once a season and once the buds have bloomed they don't make any more? This is my first year growing them and don't know much about them. Thanks for the help...

Here is a link that might be useful: