Erik,
Just be yourself. By doing so you should sound relaxed and confident. Passengers have an expectation that "The Pilot" is authoritative and knowledgeable, and that is the basis of how you should seek to deliver your announcements.
Know your audience. For example if you are operating a scheduled service it is likely that a good proportion of the passengers will be regular travellers many of whom may travel the route frequently. As such they may not want to hear for the umpteenth time a long dialogue of how many countries you will be flying over. They will want to know how long the flight will be and what time you expect to have them on stand. On the other hand, on a holiday charter where a good number of the passengers may be travelling on an annual basis, the flight will be a part of the overall holiday experience and they may well welcome a longer dialogue involving points of interest and the all the other "good stuff".
You should develop a core address and modify it with experience and as circumstances dictate. This only comes with practice, and will evolve over time. Start off by keeping the speeches fairly simple and to the point until you find a style that you are comfortable with.
As has been mentioned, be very careful with humour. Very occaisionally it may have a place, but it also has the risk of making the "pilot" appear less than authoratitive, particularly where you might later need to have instructions taken very seriously by people who now see you as a bit of a clown or a joker. It also tends to go down like a lead balloon with someone who has been otherwise mishandled or is frustrated by some aspect of their journey.
In summary: Keep it simple to begin with ; Develop your own style ; Speak in a manner that you want others to perceive you by ; Avoid the emotional pitfalls, don't try to be overtly humorous, irritated or opinionated ; Be relaxed and friendly but remember the audience expects you to sound like you are in charge of the operation.
Good luck.