Colourspace : CMYK
Vector where possible.
Minimum 300DPI resolution for Raster Images.
File Format: PDF
#1 : Colourspace
Make sure your artwork is in CMYK colourspace.
Open your printer and you'll see it contains Cyan, Magenta, Yellow, blacK ink/toner.
Artwork needs to reflect the physical capabilities of your machine.
See CMYK vs RGB Here
#2 : Resolution
Low quality artwork results in low quality prints.
Find your image DPI Here
#3 Outline Fonts
Not everybody has your fonts installed.
If you are sending artwork somewhere else without the fonts outlined, you'll cause frustration and delays.
If you've received artwork without the fonts outlined, do this Here
#4 : File & Artwork Format
PDF is king.
This one-size-fits-all format will store raster, vector, colourspace, clipping masks and basically everything your printer needs to produce the results you expect.
Sharpen up your artwork and vector where possible, see Here