Besides making a very obvious and very stupid joke that this has nothing to do with the charity Comic Relief (Red Nose Day, anyone?), I keep finding myself at a very solid brick wall when I try to write this post.
HAPPY THANKSGIVING TO ALL YOU AMERICANS FOR (now) YESTERDAY! I'm not actually American myself, so I know relatively little about Thanksgiving, but I hope you all had a nice day.
I don't actually know where to start with this. Maybe with a definition of Comic Relief Characters? Being a person who can't sit through a book without comedy somewhere, these sorts of characters are like caffeine to me, provided they don't go overboard or seem really artificial (as in, obvious that the author has just written a specific thing for them to do to bring out a (usually) lame joke).
A comic relief character is a character who provides a break from otherwise serious moments in the novel, or lightens the mood even if it's not that serious a moment, with something humorous, like Fred and George and the fireworks escapade in the fifth Harry Potter book. There are many different ways of doing them, but the one thing not to do is to make too much of an effort with them. Like with any form of humour, contrived humour almost always falls flat. If you try to make your characters funny rather than just letting it flow naturally, it ceases to be funny. There's a very fine line to strike, and, unfortunately, it's one that each and every one of you will have to strike separately. We all have our own different preferred ways of expressing humour, and the readers will too.
What is the point to a comic relief character?
Well, to be honest, exactly that: to provide comic relief. Some authors are like me and can't resist putting in something funny every once in a while. Others (are also like me and) have it as part of the character building of certain characters. If you are the sort of person who can pull off humour or a character like Merry or Pippin or the Weasley twins, then there is no reason why you shouldn't have a comic relief character in your book. It's right in your zone; it's comfortable to write; it's entertaining for both you and the reader.
However, there are probably some times when it's best not to have one -- for example, in a horror book. Also, as my mother keeps telling me (mothers are always right), even if your comic relief character shows up at a point of high tension, you probably want to keep the jokes out -- unless you're aiming for bathos or paraprosdokian (e.g. your characters have been wandering around a haunted house and they see something white and ghostly wandering around and it later turns out to be your comic relief charcter who'd had an accident in the kitchen with an enormous sack of flour). If you have a battle scene or a death scene, DO NOT start cracking the jokes. You can get away with this in a manga or if the character is GENUINELY suited to cracking jokes under pressure or normally does something stupid. If there are jokes flying around, remember that not everybody is going to respond to them well if they're in the middle a fight. They're going to be more concerned with self-preservation, for a start, and they'll be too occupied to find something exceptionally funny when distractions like laughing will put their lives completely at stake.
How many should I have?
To be honest, this is absolutely, totally up to you. If you've read the Percy Jackson books, practically every character in them is a comic relief one. You can have lots of characters as comic relief, or you can have one or two. It really, really doesn't matter. What does matter is what you do about the humour. If all your comic relief characters have identical senses of humour, they become clones and it kills the humour.
What sorts of humours should I use?
Again, this is totally up to you, and it will depend partially on your characterisation. For example, a character who might be at university studying for theology is more like to come up with a prank or joke to do with religion than somebody who spends three hours a day rowing. It's quite common to see a comic relief character who is snarky or sarcastic nowadays. That works too. The other most common type is slapstick, which is more like Fred and George. They're the forms of humour that most people find easiest to do. But really, you can go for anything -- dark humour, wit... anything. Just remember the three rules of John Cleese on humour: no puns, no puns and no puns!
I wish my brain was functioning to write more and in more detail on this, but it'll have to do for the moment. i might come back and edit.