docs: add Claude Code MCP integration guide

Add comprehensive documentation for connecting Turso databases to Claude Code using the built-in MCP management commands.

The new guide includes:
- Quick 3-step setup process
- Visual command breakdown with annotations
- Multiple usage examples (local, absolute paths, project-scoped)
- MCP server management commands
- Example natural language queries users can make

This makes it much easier for developers to integrate their Turso databases with Claude Code without manually configuring JSON files or understanding the underlying MCP protocol details.

README.md

@@ -152,6 +152,71 @@ cat << 'EOF' | tursodb mydb.db --mcp
 {"jsonrpc": "2.0", "id": 2, "method": "tools/call", "params": {"name": "list_tables", "arguments": {}}}
 EOF
 ```
+
+#### Using with Claude Code
+
+If you're using [Claude Code](https://claude.ai/code), you can easily connect to your Turso MCP server using the built-in MCP management commands:
+
+##### Quick Setup
+
+1. **Add the MCP server** to Claude Code:
+   ```bash
+   claude mcp add my-database -- tursodb ./path/to/your/database.db --mcp
+   ```
+
+2. **Restart Claude Code** to activate the connection
+
+3. **Start querying** your database through natural language!
+
+##### Command Breakdown
+
+```bash
+claude mcp add my-database -- tursodb ./path/to/your/database.db --mcp
+#              ↑            ↑       ↑                           ↑
+#              |            |       |                           |
+#              Name         |       Database path               MCP flag
+#                          Separator
+```
+
+- **`my-database`** - Choose any name for your MCP server
+- **`--`** - Required separator between Claude options and your command
+- **`tursodb`** - The Turso database CLI
+- **`./path/to/your/database.db`** - Path to your SQLite database file
+- **`--mcp`** - Enables MCP server mode
+
+##### Example Usage
+
+```bash
+# For a local project database
+cd /your/project
+claude mcp add my-project-db -- tursodb ./data/app.db --mcp
+
+# For an absolute path
+claude mcp add analytics-db -- tursodb /Users/you/databases/analytics.db --mcp
+
+# For a specific project (local scope)
+claude mcp add project-db --local -- tursodb ./database.db --mcp
+```
+
+##### Managing MCP Servers
+
+```bash
+# List all configured MCP servers
+claude mcp list
+
+# Get details about a specific server
+claude mcp get my-database
+
+# Remove an MCP server
+claude mcp remove my-database
+```
+
+Once configured, you can ask Claude Code to:
+- "Show me all tables in the database"
+- "What's the schema for the users table?"
+- "Find all posts with more than 100 upvotes"
+- "Insert a new user with name 'Alice' and email 'alice@example.com'"
+
 </details>
 
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