See Using External JavaScript Libraries. Basically, you can include the file, and then call a script after it loads. I've included the example from the manual below. As you can see, once imported, they are exposed as normal objects/methods. You don't need to do anything "special" to gain access to the objects, as they appear as part of the controller/helper's namespace.
Component
<ltng:require scripts="{!$Resource.chart}"
afterScriptsLoaded="{!c.setup}"/>
<canvas aura:id="chart" id="myChart" width="400" height="400"/>
Controller
setup : function(component, event, helper) {
var data = {
labels: ["January", "February", "March"],
datasets: [{
data: [65, 59, 80, 81, 56, 55, 40]
}]
};
var el = component.find("chart").getElement();
var ctx = el.getContext("2d");
var myNewChart = new Chart(ctx).Line(data);
}