How do I pass multiple attributes into an Angular.js attribute directive?

You do it exactly the same way as you would with an element directive. You will have them in the attrs object, my sample has them two-way binding via the isolate scope but that's not required. If you're using an isolated scope you can access the attributes with scope.$eval(attrs.sample) or simply scope.sample, but they may not be defined at linking depending on your situation.

app.directive('sample', function () {
    return {
        restrict: 'A',
        scope: {
            'sample' : '=',
            'another' : '='
        },
        link: function (scope, element, attrs) {
            console.log(attrs);
            scope.$watch('sample', function (newVal) {
                console.log('sample', newVal);
            });
            scope.$watch('another', function (newVal) {
                console.log('another', newVal);
            });
        }
    };
});

used as:

<input type="text" ng-model="name" placeholder="Enter a name here">
<input type="text" ng-model="something" placeholder="Enter something here">
<div sample="name" another="something"></div>

You could pass an object as attribute and read it into the directive like this:

<div my-directive="{id:123,name:'teo',salary:1000,color:red}"></div>

app.directive('myDirective', function () {
    return {            
        link: function (scope, element, attrs) {
           //convert the attributes to object and get its properties
           var attributes = scope.$eval(attrs.myDirective);       
           console.log('id:'+attributes.id);
           console.log('id:'+attributes.name);
        }
    };
});

The directive can access any attribute that is defined on the same element, even if the directive itself is not the element.

Template:

<div example-directive example-number="99" example-function="exampleCallback()"></div>

Directive:

app.directive('exampleDirective ', function () {
    return {
        restrict: 'A',   // 'A' is the default, so you could remove this line
        scope: {
            callback : '&exampleFunction',
        },
        link: function (scope, element, attrs) {
            var num = scope.$eval(attrs.exampleNumber);
            console.log('number=',num);
            scope.callback();  // calls exampleCallback()
        }
    };
});

fiddle

If the value of attribute example-number will be hard-coded, I suggest using $eval once, and storing the value. Variable num will have the correct type (a number).