The general theory of ritual magic is that, if you're using a normally combat oriented spell in a non-combat situation, you are able to make it more powerful than normal (or even just different).
For example: You have a captured gnoll. The prisoner is immobilized and completely at your mercy. In theory, you could simply cast dominate person until it works. However, this doesn't make for a particularly good story, nor does it make efficient use of your limited uses of dominate person per day - you've got all the time in the world, but having to give up and try again tomorrow is annoying. So you cast the spell as a ritual, taking extra time and putting extra effort into the casting, and it works the first time with no chance of failure. (Footnote: this could still fail, of course. For example, if the gnoll was actually a shapeshifted dragon that was merely pretending to be captured, then - unless its will save is abysmal - the ritual would fail.) Think of it as forcing the subject to take ten, or take a one, on their will save.
Here's another example: You want to travel in style from point A to point B. A riding gryphon would be perfect. Now, you can summon a gryphon with a normal summon monster spell - but that would only last a minute or two, not long enough to get anywhere with it. So you draw out a summoning circle, burn a few candles, and summon a gryphon to serve as a steed that will last a few hours. Of course, it'll fade out pretty quickly if you get into combat...
So, the question I've gotten most so far is "Um, okay, what do I actually have to do to make this a ritual?"
The answer is: whatever you want. Pretend you're on stage, and have to ad-lib casting a powerful spell. Drawn runes are good. Candles are good. Incense, eye of newt, bubbling cauldrons. Calling on the names of dark gods and things best left forgotten. Even just standing there and meditating is fine, if that's your character's style.
Be creative! Have fun with it; ritual spells are your chance to show off your character's magical style. (Not that you shouldn't show off that style in normal spells, of course, but combat spells have to be practical things - a quick gesture, a few words of power - and that does tend to be somewhat limiting.)