WLED is an open-source, DIY software. This means all services are hosted locally on your ESP8266. Because of this, you can only control your lights from within your local (home) network.
If you need to control WLED from anywhere (the public internet) you can do so in multiple ways, some requiring additional hardware:
1. Use Blynk
From version 0.7.1, WLED supports the free IoT cloud Blynk! See this for details! It has a nice app for you to control the lights from anywhere!
2. Use an Amazon Echo device
If you have set up your Alexa device to control WLED, you can just use the Alexa App or another Echo device linked to your account to control your lights (on/off and brightness only)
3. Create a Port Forwarding
Warning: An insecure HTTP connection is used, please do NOT edit sensitive info like the WiFi settings when connected via the port forwarding!
This method offers more flexibility, but is also more involved.
Keep in mind this causes anyone with your IP address to have access to your ESP8266!
Setting up an OTA lock password is a must to prevent attackers from acquiring your WiFi credentials!
To expose WLED to the internet, create a port forwarding for your ESP's IP in your router configuration. If your public IP changes a lot, make sure to also use a dynamic DNS service so your lights are always accessible. Unsure what any of this means or how to do it? Google for "[your router model] port forwarding"!
Additionally, this opens up many new possibilities for automation! You can use a service like IFTTT Webhooks to send automated WLED API calls that can do anything from turning on the lights at a set time to changing their color if you get a new email!
4. Use hue sync
If you have a Philips hue setup and sync WLED to it, you can control your WLED lights in any way it's possible to control your hue lights (hue App, Alexa (including colors), any other service that uses Philips hue API)