I guess it can be like the matrix. It depends, really. Your first few lucid dreams will be different from the ones you have when you've gotten used to them (especially the first one).

If you're motivated to learn how to do it, and follow some of the tuturials on this site (or elsewhere), you'll eventually have your first lucid dream. You'll realize as soon as you become lucid that you were 100% sure you were awake before you did. It's like if you were to realize you're dreaming right now.
Of course, you'll be amazed and maybe overwhelmed by this experience. That's why there's a chance you'll wake up right away the first time (many people do), but if you stay calm and use a technique to prevent awakening (like for instance rubbing your hands together), you could stay in the dream. At this point you'll have the chance to look around more calmly and notice how amazingly real (or strange) everything looks, sounds and feels. Maybe you can even do something cool like walking through a wall or flying.

After a while, when you've had more lucid dreams, they won't catch you by surprise as much, and it'll become easier to stabilize. However, the experience is always amazing to some extent, unless, maybe, if you're so good you can practically do it at will. One of the lucid gods would have more to say about that.

Of course, this is just my experience. I'm not you, and there's no telling what your exact lucid dreams will look like. I would just recommend to you to practice some of the techniques so you can see for yourself. LD's come in all sorts of forms for all sorts of reasons.