Knowing your audience may be the most important thing to keep in mind when composing a funny speech. Even if certain things are funny to you, if they don't fit the overall tone of the event or the tastes of the people present, you risk stony faces, awkwardness, or even giving offense. Pushing the boundaries of what's acceptable to laugh at might be great for stand-up comedy, but it's not appropriate, for example, at a children's party. Knowing your audience isn't just restrictive, though; it may provide an opportunity for "insider" humor. Just make sure you're appealing to the whole audience and not leaving anybody out.
Unless you're planning on dropping in just a few jokes here and there, set a humorous tone right away. If you don't, you may leave your audience confused, especially if your sense of humor tends to be dry. If you're asked to speak at a wedding, and open with, "I feel kind of embarrassed; up until a moment ago, I thought this was a birthday party," you've created a precedent for humor. If you make the same comment after earnestly congratulating the bride and groom, you may encounter some puzzled looks.
Create a character for your delivery of the speech. This can be as explicit as speaking as a historical personage or a well-known comedic character from television or film, or as subtle as modifying your own personality only slightly. You can present your speech as an obviously over-the-top "nervous speaker" character, or a "wasn't-invited-to-the-event" character. Use this one wisely: it takes commitment and is probably not appropriate for all occasions. Also, at some point, you may have to break character to deliver your more sincere messages.
Whatever you prepare ahead of time, don't get too attached to it, and don't become rigid in how you imagine your speech will go. Humor only works if you get a real, spontaneous reaction from the crowd. If you start into a joke and you find the audience unresponsive, be ready to switch your approach and respond to the moment. If a joke bombs, don't worry. A casual sense of humor about yourself and the failed joke, combined with a willingness to adjust and move forward with the speech, will communicate a sense of warmth and ease to the audience.