Here are step-by-step set up instructions for connecting your Apple TV and your wireless router. Note, Apple has discontinued making the Airport Express, but they are still available through Amazon. There are alternatives to the Airport Express discussed in the Hardware section of this site. Before telling you how to make the connections, let's talk about the why: "Why do I want the option of presenting wirelessly?"
As you already know, your iPad has the ability to connect to a wifi signal. It also has a feature called "Airplay Mirroring", which allows you to project the "mirror image" of whatever is on the screen onto a projector. So rather than having your iPad tethered to a cable that connects to the projector, why not have the freedom of moving around the room with your iPad in hand? A wireless connection, utilizing the iPad's ability to connect to a wifi signal, gives you that power, flexibility, and control.
The Apple TV is made for the iPad. It is the "Screen Mirroring" icon that you are looking. For iPads that run on iOS 12 or later, swipe down from the upper-right corner of the screen to bring up the AirPlay menu. You will see the image set forth below. Touch “Screen Mirroring.” For iPads that run on iOS 11 or earlier, swipe up from the bottom of the screen to bring up the AirPlay menu. Then touch “Screen Mirroring.”
Now touch “Screen Mirroring.” When an Apple TV is connected to the same wireless connection as your iPad, it will show up when you touch the Screen Mirroring icon, indicating it is ready for project your iPad image.
Select your Apple TV
Now select your Apple TV [BOB’S APPLE TV in this image]. Your iPad will now connect to the Apple TV and the screen of your iPad will be “mirrored” on the projected screen or the external monitor.
Many presentation locations have existing wireless networks. But they can be unreliable. When we are projecting wirelessly, we are sending the image from our iPad wirelessly over the internet to the Apple TV. The Apple TV, using a simple HDMI cable, is hard wired to your projector. So as long as our Apple TV in setup mode, is linked to the same wireless network as our iPad, and as long as we have selected our Apple TV in the "AirPlay Mirroring" window set forth above, we can project wirelessly. But here is where the Airport Express comes into play.
The Airport Express (or other brands of wireless routers) creates its own wifi signal when you turn it on. This signal does not allow you to get onto the outside world internet, but you don't need to do that for our purposes here. Rather, you simply want to connect your Apple TV and your iPad to this same wireless network, one that only you are using for your presentation. To make things really simple, and to make the connection between the Airport Express and the Apple TV as fast as possible, connect these two devices together using a simple Ethernet cable as depicted below. Use a short cable, less than a foot long, if possible.
Connecting Apple TV to Airport Express (or another wireless router)
We use a simple Ethernet cable to "hardwire" these two devices together. Note that you need to plug the cable into the correct port, depicted above, on the Airport Express--the one with the little round circle above it.
Remember, your Apple TV is now "hardwired" to your Airport Express, so you don't need to worry about making a wireless connection between those two devices. That is why we use an Ethernet cable--simpler and faster.
Make sure your that in your wifi settings on your iPad, you select the name of the network that your Airport Express is creating, in this example, “WIR-Secure” (see image below):
Connecting your iPad to the wifi network created by your Apple Express
We need to have our iPad on the same wireless network--wifi network--as our Apple TV. By making this connection in your "Settings--WiFi", and by selecting our Apple TV from the "Airplay Mirroring" menu depicted above, we are now able to project whatever is on our iPad over our projector. Oh, let's finish the projector or TV setup.
The final step is to connect our Apple TV to our projector or TV monitor. This is simple. We use an HDMI cable, plugging it into the back of the Apple TV and into one of the HDMI slots on the back of the projector. Remember, this is why we purchased a projector that has an HDMI connection--the current state of the art. Then when we turn our projector on, we just need to make sure that we select the same HDMI output slot as we have used for our plug since most modern projectors have more than one HDMI output.
Connecting your Apple TV to your TV monitor or Projector
This is a simple HDMI cable connection. Here, you may want to have more than one length of HDMI cable. Sometimes you can place your tethered Apple TV/Airport Express right next to the projector, and sometimes you can't. Carry more than one length with you so you have flexibility in the setup process.