Here's a pre-tip to start: Don't say anything if you don't have something to say. Worship leaders have got to stop feeling the pressure to be speakers. Assuming you have something to say…
Here are 2 quick, very logistical tips for worship leaders regarding talking between songs:
Tip #1: If you're on in-ears, take one in-ear out when you go to talk. Always. It helps you hear what your voice sounds like in the room which feels much more natural and not as loud. And it let's you hear the subtle feedback from the crowd. If they snicker (or gasp), you can hear it and respond realtime. Keeping both in-ears in while singing works because you're mostly listening to your band. When you're talking, you want to listen to the crowd. Otherwise it's one-way, and they can tell.
Tip #2: Try to ignore the microphone. Somehow we do this when singing, but not when talking. Talk into it the same as when you sing. Speak out to the crowd. If you rely on the microphone to carry your voice, you won't exert. Then you sound like you don't mean it. Imagine you have to talk to the crowd without the mic. If this makes you talk louder than you sing, back off until they match. Ask someone you trust for input.
This is painfully practical for me to even type (seriously, I want to delete this and do a more "spiritual" post right now). And it can even feel fake to pay so much attention to details like this. But that's the whole thing. There's technique involved in coming across in reality the way we come across in our heads. The goal should always be to be as real and honest as possible. So don't go overboard with these and become obnoxious and fake! ;) But just a couple of subtle tweaks can change your tone and make what you have to say more audible and more importantly, believable.
Hope that's helpful.