The short process is: meet someone who works at the OED evaluating new words for inclusion. The slightly longer process involves plying him or her with drink. The most complete answer is contained in Lyza Danger Gardner's blog entry How I Got a Word into the Oxford English Dictionary. (And yes, it includes both of the aforementioned steps.) As Erin McKean pointed out in her Ten Things You Should Know About the Dictionary, it helps to have identified a lexical gap first -- a place in the language where a word does not exist, but a need is clear. And that's exactly what Lyza did...though the word she got into the OED was not quite the one she'd planned on. Here's a snippet:
...I wanted him to consider the word "nugry," promoted by my friend Tom, who was active on (I believe) alt.puzzles or somesuch similar problem-solving-related newsgroup. The definition of nugry? Essentially: "The third word in the English language ending in '-gry'", existing for the sole purpose of being an answer to a puzzle-riddle I've long since forgotten. You can see why I failed in this regard.
Besides, William [the OED editor] was fairly nonchalant (at best) about his occupation. He found it bemusing that I held such reverence for the establishment. "Eh," he would say, "really we're all just a bunch of tossers."
One night we went to London to celebrate William's birthday. We all went to a pub in Camden Town called, if memory serves, the Ram and Tup (a rather bawdy reference!). Everyone got fair well plastered except myself and Matt. We trundled William into the back of Matt's car, all spinny-headed and dreamy. I was sitting in the passenger seat.
"Lyza. I have something that is going to make your week."
"Your word is going to be in the next edition."
"Except not the one you think." ...
Read the rest to find out which word actually made it into the dictionary, thanks to Lyza's perseverance.