While Adobe Illustrator isn't the first tool one thinks of for printing envelopes, there's nothing keeping you from doing so, provided your printer driver allows you to specify a manual paper source. You will need to be creative within Illustrator to make the artwork fit the available area, but printing on an envelope is the same as printing on a custom paper size.
Open a new piece of art, and specify that the size is Custom and the units are Inches.
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Enter the dimensions of the envelope you're using. For a standard business envelope, this would be 8.5 inches wide by 4 inches tall.
Create your artwork in the artboard specified. You may wish to leave margins of a quarter of an inch.
Load the envelope in your manual feeder in your printer, and in Illustrator, hit "Ctrl+P." Click on the "Setup" item in the Print dialog box, and specify that the X coordinates be "+4 inches" (or whatever the height of your envelope is). Hit "Done" and then hit "Print".
Things You'll Need
Printer with a manual feed option
To make sure your artwork aligns properly, print to a full sheet of paper through your manual feeder as a test print.