To save your Illustrator document as a 300 DPI PNG or JPG image, go to File>Export>Export As… and choose your preferred file format, that is JPG or PNG. In the options dialog box, click the resolution drop-down and select “High (300ppi)”. Then click ok. If you are saving as an Illustrator file as vector .ai, .eps or .pdf, make sure you set up your document as 300 DPI in your new document options. If you didn’t do this at the start, create a new document File>New… click advanced options, and select “High (300 PPI)” in the Raster Effects drop-down list.