GASP! Well it's quite simple, really! You pick a piece of art you feel is worthy of a DD (see examples here: [link]) and then you go to this page to find someone to send it to: [link]
Every gallery has a 'Gallery Moderator' (or 'Community Volunteer') who takes DD Suggestions - you just send them a note! More detailed instructions are also on that help page, and sometimes the moderator will have a special set of instructions on their dA page telling you how to submit/suggest a DD!
I hope that helped a little - and if not, let me know, and I will clarify!
I've only felt compelled to suggest a DD twice, because although I come across a lot of amazing artwork most of it either not impressive enough, in my opinion, to suggest or the deviant has quite enough views and watchers already. The first time I suggested a DD I had to revoke it because I didn't realize the artist had received one in the past 3 months(3 months is how long until you can be suggested again right?). The second time I was unable to revoke it before I realized someone had suggested it already.. I am obviously terrible at suggesting