I was wondering if this shield has similar programming to other WiFi shields?
It's completely different from any other WiFi Shield. The communication with the shield is similar to the much more poplar and cheaper ESP8266 shields in that it uses AT commands sent over serial but the actual AT commands are different.
found some documentation on it that seemed pretty in depth.
In depth on some things but not the most important: How to actually use the thing! For that they direct you to a forum thread that happens to link to the manufacturer's PDF manual, which is in a repository claiming to be an Arduino library when really it's nothing of the sort. Once you find it the manual seems to be pretty good though.
they go into AT mode and AT-STAT mode, and I don't really know what any of that is.
Be careful! It's not "AT mode and AT-STAT mode", it's AP mode and AP+STA mode. Only a couple letters difference but precision is extremely important if you want to be successful with programming and electronics. AP stands for access point. This means you can connect devices directly to the shield over WiFi without the need for an external network. STA stands for station. In station mode you will connect the shield to an access point, such as your WiFi router. AP+STA mode means operating in AP and STA mode.
At the end of the documentation, they have a sample code that has the shield sleep. I still don't really know what that means.
The shield will use a lot of power when it's running. This is especially a problem when you're using a battery as a power source for your project. By putting the shield in sleep mode you will drastically reduce the power consumption, but will not be able to use the thing while it's asleep. So if you only need to intermittently use WiFi then you can leave the shield sleeping until you need to communicate over WiFi, then put it back to sleep as soon as you're done.
Is the sample code at the bottom of the link I shared similar to how other WiFi shields are configured?
No, it's very specific to that shield. It's only showing how you can control the sleep state and also check the sleep state by writing and reading to specific pins that are connected to the shield. It doesn't demonstrate how to actually use the shield for communication at all. Evidently dfrobot decided that wasn't important information to document. I have a bad feeling about this shield. The price is very high and it doesn't seem that dfrobot has made a real effort to provide good support for it, especially considering the price. I would expect better documentation, example sketches and a library that is compatible with the standard Arduino WiFi library API as much as possible. I think a $7 ESP8266 shield would be a better choice. They are not perfect but you will find much better community support in the form of forum threads, tutorials, libraries, example sketches, and people who can answer your questions. On the other hand, I don't know that the sleep capabilities of the ESP8266 are very good, especially as controlled via AT commands so if that's important to you then the dfrobot shield may be a better choice.
There are other options that may offer higher performance than either the dfrobot or ESP8266 such as the Arduino WiFi 101 Shield. It's a little bit more expensive than the dfrobot but I think the official support will be a little better. I'm not sure about the community support, I don't see it mentioned very often here on the forum.