Hook, Line, and Sinker
This technique is a little devious, so only use it if your significant other already has at least a passing interest in fantasy or science fiction, or you risk turning them off from the genre altogether. This trick sealed the deal for me, so don't underestimate its efficacy. The idea is to buy them a book, which is the first in a long series, and get them hooked. Think Mercedes Lackey or Robert Jordan. At a certain point your significant other will attain critical mass and go out and get the rest of the series on their own. From experience, I chose the Wheel of Time for this task, as the characters really tend to draw you in. I am proud to report that my girlfriend is on book four and progressing at a respectable pace.
The Great Unknown
This trick, if it can even be called that, should be used regardless of the situation: keep them in suspense. Feed them little interesting tidbits from the book and leading questions. Try "I bet you can't guess who dies", even if no one dies. Ask them what part they are on and tell them that an amazing chapter is coming up--in brief, do whatever you can to keep them interested. My personal favorite, as alluded to, is the fake plot twist. Throw out something totally ridiculous that absolutely doesn't fit with the story, and they will keep reading just to prove you wrong.
Tried and True
Tried and True
This is advice I shouldn't have to give, but I'll put it out there just to be clear. Don't pick something radical that embodies all the excesses of the genre, make sure to go with a book that will allow your significant other to gently suspend their disbelief, and not try to wrestle it away from them on the first page. If you can, avoid books with overly dramatic prologues that throw around a lot of technical jargon. As a rule, it should be a book that will ease them into the genre as gently as possible, and not try to explain the Seven Principles of Magic in the first fifty pages.
The Book Swap
This trick is simple and sweet. Simply promise to read one of their favorite books in exchange for one of yours, even if it's Ayn Rand. Voila!
Draw connections between books that you know they already like. "Oh yea, that's so similar to X Great Fantasy book I read, I bet you would like it". This trick is best applied discreetly and in small doses, as abusing it tends to make you sound preachy. This works with pretty much any element of a book, so make sure your comment is intelligent and actually relevant to the book your significant other is reading.
This is by far my favorite trick: Simply point out to your significant other that they have already read a science fiction or fantasy book, and that they absolutely loved it. A good example that comes to mind is The Time Traveler's Wife; obviously, it isn't your typical science fiction book, but play up the similarities to other great science fiction, and you'll have a convert on your hands in no time. Alternately, give them just such a book to read if you think they aren't ready for a more intense 'genry' stuff.
The Wheel of Time Turns
The Wheel of Time Turns
If none of these tricks worked, don't sweat it, time is on your side. Determined application of these rules will get you there in the end, and if it doesn't, than it wasn't meant to be--just go ahead and find yourself a new significant other. You might want to try the SF/F section at the bookstore.
Remember, none of these tricks are going to work overnight. They take a fair amount of time and effort, so don't get discouraged. Above all, be subtle and understanding, and don't try and force your love of science fiction or fantasy onto your significant other--if anything, they will come to you and ask where to start when they are ready.
Do you have any tricks of your own that have worked for you in the past?