Good to hear from you. You’ll find a whole bunch of iPad enthusiasts in this Forum who are only too willing to help other iPad owners and to hear of their experiences. Don’t be afraid to post any questions you may have or use the ‘Search’ button near the top of the Forum web page. I usually find I discover one new interesting and useful piece of information about my iPad every day - and often not even what I was looking for!!
As you probably know, you can purchase an iPad dock-to-VGA accessory for your iPad to enable you to connect it to video projectors etc. That's the good news!! The bad news is that this accessory is only supported by certain apps - such as Apple's Keynote (PowerPoint) app - i.e. it is not a 'universal' accessory that simply projects the iPad screen, it needs to be explicitly supported by the app. There is more information, including some good and bad comments, here...
Apple iPad Dock Connector to VGA Adapter - Apple Store (UK)
So, if you simply want to project, say, lectures for your students using conventional PowerPoint slides there's no problem (though it's not a wireless solution). But if you want to project the output of other apps then you'll need to determine, on an app-by-app basis, whether they support the iPad's video output accessory.
In terms of wirelessly connecting your iPad to a video projector, I am unaware of any way that this can be done. The apps in the iPad are 'sandboxed' - in other words they have very limited interaction, unlike in the PC environment. The advantage of this is that an iPad should be effectively protected from viruses. The downside is that it is probably impossible for anyone to develop an app that could be used to project the iPad's screen wirelessly. There are far more experienced Forum members out there who will be able to shed more light on this but, without jail breaking your iPad, I suspect you are limited to using the iPad dock-to-VGA adaptor.
Once again, welcome to the Forum. Enjoy your iPad and I hope that your students enjoy their lectures too.
Tim
Scotland