How to access the user's ExtendedAttributes after a GET REST API request

Like all REST requests, you can use the response object in your success handler. I'd recommend using a debugger to inspect what it contains. As an example, here's your code outputting properties of the response object including the User and the User's ExtendedAttributes to the browser console.

jQuery.telligent.evolution.get({
	url: jQuery.telligent.evolution.site.getBaseUrl() + 'api.ashx/v2/users/{id}.json',
	data: {
		Id: context.userId
	},
	success: function(response) {
		// render user
		console.log('User object:')
		console.log(response.User);

		// render user's extended attributes
		if (response.User.ExtendedAttributes && response.User.ExtendedAttributes.length > 0) {
			console.log('Extended attributes:');
			console.log(response.User.ExtendedAttributes);
		} else {
			console.log('No extended attributes.');
		}
	}
});