Eat waffle, don't write it.

Strong prose is immediate, concrete and precise.

I know a strong prose helps the reader become immersed in the story, but like many writers my first draft is full of waffle.

How to cut the fluff?

Immediate - 
Active verbs not passive. I was going to the shop = I went.
He half-ran  = He jogged / trotted
He continued to walk forward = he strode
She knew she needed = She needed
I thought I wanted =I wanted
He began to sneeze = He sneezed

Concrete -
Evoke senses, be tangible.
Show not tell. 
Rather than describing the library as immense, describe what the character sees, smells, hears, notices. This will not only feed the reader's imagination but tell the reader something about the character.

Precise -
Choose your words carefully.
Every word adds to the story.
Usually it means using fewer words, cutting your first draft by 20%. He ran very quickly =he dashed.
If you use the generic word such as dog or boat or flower - the reader may imagine something different from you. Mastiff, Gondola, Daisy are precise.
Replace explanatory phrases with a word. The clouds dropped their heavy load of water =It rained.