Getting someone a Rubik's Cube? Shame on you. That's a horrible thing to do. If you must do it, also give them this list of links to online guides to solving the tiny cubic bundles of frustration.
In truth, I know I'm not giving out instructions for a Rubik's Cube giver. I don't think there are any Rubik's Cube givers. I think these things are actual evidence that Santa Claus is real. Almost everyone I know has one, or has had one at one time, but no one knows how they got it. It just appears in people's homes and taunts them. If you're stuck with one of these things, there is help available. If you're the mysterious giver, knock it off.
Be careful online. There are a few sites which say they'll help you, and then leave off the last couple of steps unless you buy their book. Which you will. With shaking hands. Through your tears.
A good, complete source for beginners is Peter Still HQ. That link gets you to a page of instructions that should allow you, with some practice, to finish up a Rubik's Cube in sixty seconds. There's even a PDF copy of instructions for easy printing. The maintainer looks to be a genuine Rubik's Cube enthusiast, and has links to his involvement in the 25th anniversary, links to other Rubik's Cube sites, and translations into Italian, German and Spanish. There are minor problems for the diagramatically challenged, those who don't like walls of text, and for hesitant beginners. The first few sentences of the solution section are, "I believe that the first layer should be done intuitively. You need to understand it and solve it without learning algorithms."
Your next stop is Chess and Poker, where you'll find a seven step solution. The article is less personal and more blankly instructional, but many will find this comforting. (Often you feel like you're letting Peter down.) It can be intimidating to wade through the three thick paragraphs of terminology and move notation at the top. The slog through notation pays off, though, when further down all the algorithms are spelled out in shorthand notation beneath each section. With the moves plotted out like that, it's a cross between a puzzle exercise and a dance lesson.
For those who really can't stand reading the diagrams and need to see something kinetic to learn, there's one last resource. This series of instructional videos at Video Jug is a good resource. It gives you a dynamic view of solving the cube and can be listened to over and over if you need to look down at your cube and not up at the screen. It's even got celebrity Rubik's Cuber Chris Dzoan showing you how to solve a cube. The problem? He's a celebrity because he can solve a cube one handed. In under seventeen seconds. If that doesn't break your spirit, I don't know what will.
Good luck in your personal quest to solve your personal torment. With hours of practice, eye strain, carpal tunnel syndrome and, I'm guessing, one depressive fit so deep that you're drinking mouthwash, you too can live to see your cube returned to its original condition.