While I don't speak myself (publicly or in a screencast) often, I have witnessed many others over the last 5 years. This is what i've learned:
Know the content inside and out - listeners or attendees will be able to tell if you know what your doing or not, regardless of if they know anything about the subject prior to watching / listening. It'll come through in your tone of voice.
Be prepared - if you're speaking in person, be prepared for people to ask questions. If you're doing a video and comments are allowed - just the same, people will ask questions. With a video you'll get a bit of time to research an answer - in person, you'll be on the spot.
I would definitely prepare some sort of document with major points, sub points and notes for each. It doesn't need to be a script and again, people will be able to tell if you're just reading off of paper - but enough that you can get through the video, read which point you're on, then explain / do the point in the video / live.
Practice, practice, practice. As I said, I don't do this myself often - but I did a video for my website. I wanted to explain the new content editor, how it worked, it's benefits, etc... I too, am self conscious about my voice and what I feel is a very minor speech impediment. I must have recorded the video 30-40 times before I was happy with the outcome - it came out to about 10 minutes long.
Equipment wise, the camera in any recent Mac will suffice if you intend to be apart of the shot. I can't speak of microphones - the built in mic on a MBP worked fine for me - and screen recording software is wide and varied you should be able to find an appropriate one for Mac or Windows.
On a Mac, I use this to record the screen and it's worked well.