Stream AI Responses in Real-Time

I want my app to stream AI responses word-by-word, like ChatGPT does, instead of waiting for the entire response.

Framework: [Express, Django, FastAPI, Next.js, etc.]
AI Provider: [OpenAI, Anthropic Claude, or describe your setup]

I want:
1. User submits a prompt through a text input
2. The AI response appears word by word in real-time (streaming)
3. A "thinking..." indicator while the first token is loading
4. The ability to stop/cancel the stream mid-response

Show me:
- How to set up streaming from the AI API
- How to push each chunk to the browser as it arrives
- The frontend JavaScript that displays tokens as they stream in

I'm new to streaming and WebSockets, so explain the connection between them simply.