question about dx lenses

[chad79]

Hi there just got afew question about nikon dx and d series lenses.
Are dx lenses designed for crop sensor dslr such as d300?
So if i get a 20mm dx lens will it be 20mm or will it be something else on a d300.
D series lenses, are they designed for full frame dslr or cropped?
I know when i put on a d series lens on my d300 it is not what it is.