How do I extend the range of my airport extreme

A few guidelines here.......

You will obviously need an extender located outside or just inside the outside wall of the house to be able to extend the network to an outdoor area. Some experimentation for the best location is usually required for setups like this.

The new extender will need to be able to pick up a strong wireless signal from the AirPort Extreme, assuming that it will use wireless to connect. Things would be much better if the extender could connect to the AirPort Extreme using a permanent wired Ethernet cable connection. Then, you don't have to worry about signal loss over a wireless connection between the Airport Extreme and AirPort that is extending.

Since Apple designed their "extend" feature to only work with other Apple routers, you'll need either another AirPort Extreme.....(best performance)......or another AirPort Express to extend the signal outdoors.

Although Apple discontinued the AirPort line over two years ago, AirPort Extremes and AirPort Expresses are still available as new, refurbished, and used products on sites like Ebay and Amazon.

Rather than buying more Apple products second hand or greatly inflated prices.. since Apple has left the router building.. 2.5years ago.. it is actually time to move on.

Mesh products are what Apple sell now.. from Netgear Orbi, Amazon Eero and Linksys Velop. (obviously you can buy these anywhere so choose who you prefer to buy from). Mesh comes in various kit and speed levels and can easily grow to cover your house and backyard in a way that will work far better than older Apple routers. (which had their last design outing in 2011-12.. much water under the bridge since then.)