How to Encapsulate and Create Maintainable JavaScript

Your question can't be answered that easy, because some information is missing. Which methods use which of the attributes? It's a problem which should be solved when analyzing the problem (not in the design, and definitely not in the code). So which part of your code do you whant to decouple from which other part?

To answer the question on a more general level:

It's regarded good Object Oriented Design (OOD), if you reach a high cohesion inside one module and low coupling between modules. In your case this means: if all your methods reference all your attributes, then keeping it all in one big file is regarded good OOD. But normally the real world problems aren't wired in such a monolithic way.

If you want to decouple something, there is the Single responsibility principle stating, that you should decouple the parts that don't interact with each other. In your case you could (maybe) put everything regarding attribA into one module and anything regarding attribB into another module. Thus it won't get messed up, regardless of the concrete module implementation you use.

Well, the approach I take at least in terms of readability is to pull the function declarations out of the return block:

Sm.screenfragment(function (screen, viewModel) {
    //Still can grow into a mess
    var util = {
            attribA : screen.get('title'),
            attribB : screen.get('status'),
            setAttribA : function (container) {
            //Do Stuff
            },
            setAttribB : function(event, viewName) {
            //Do Stuff
            }   
    };

    var create = function() {
        //Do Stuff
        util.setAttribA...
    };

    var prepare = function(callback, config) {
        //Do Stuff
    };

    var enter = function() {
        //Do Stuff
    };

    var exit = function(callback) {
        //Do Stuff
    };

    return {
        model: {
            //Do Stuff
        },
        create: create,
        prepare: prepare,
        enter: enter,
        exit: exit
    };
});

And then if the code within those functions is generic/modular, pull that code out into a utility file and call them from there

I agree with @Waog that good OOD is probably the solution to your problem. Given that you might have a lot of properties on the object that you're writing setAttribA functions for, why not use a map to clean up the code a bit? There are probably dozens of map implementations for JavaScript, a simple google search for "map polyfill" lead me to this one, which looks nice: http://eriwen.github.io/smap.js/

Seems like there's opportunity to use an OO approach to encapsulate similar functionality. Each class can live in its own file... This seems nice:

// In file attrs.js
function ScreenAttrs(screen) {
    this.screen = screen;
    this.attribA = screen.get('title');
    // ...
    // ... could even categorize attributes into separate methods
    // this.initFooAttrs();
    // this.initBarAttrs();
};

// In file modifier.js
var attrs = new ScreenAttrs(screen);

function AttribModifier(attributes) {
    this.attrs = attributes;
};

AttribModifier.prototype.setAttribA = function() {
    // .. do stuff w/ this.attrs.attribA
};
// ... etc.

// in api.js
var modifer = new AttribModifier(attrs);

function ScreenAPIImpl (modifier) {
    this.modifier = modifier;
};

ScreenAPIImpl.proxy = function(context, method) {
    return function() {
        return method.apply( context, args.concat( slice.call( arguments ) ) );
    };
};

ScreenAPIImpl.prototype.model = function (foo) {
    // operation with this.modifier.setAttribA
    // operation with this.modifier.attrs.attribA
};

ScreenAPIImpl.prototype.fetchAPI = function (screen, viewModel) {
    return {
        // Bind context of method to this object instance
        model: this.proxy(this, this.model),
        // ...
    };
};

// .. etc

var api = new ScreenAPIImpl(modifier);

Sm.screenfragment(api.fetchAPI(screen, viewModel));

This also opens itself up to creating a helper builder class that constructs everything and returns the final API object:

var api = CreateAPI(screen);

Let's consider the following excerpt from your code, where I understand the issue lies:

Sm.screenfragment(function (screen, viewModel) {
    //This can grow very quickly and turn into a mess
    var attribA = screen.get('title'),
    ... 
    ... 
    attribZ = screen.get('status');

    var setAttribA = function (container) {
        //Do Stuff
    };
    ...
    ...
    var setAttribZ = function(event, viewName) {
        //Do Stuff
    };

    ...

As far as I can see what you're doing, in my opinion, it's unnecessary to define properties attribA up to attribZ and then setting them, and then again define setter functions for them. You could simply return or access screen.get('x') where and when it is needed.

But if it's absolutely necessary, for some reasons, then the following strategy popularised by jQuery may suffice:

attributeX = function(x, container){
    // if x and container are undefined, then we can assume API caller intends to
    // read value of property 'x' otherwise, caller intends to write to the property.
    if(container){
        // don't forget to do stuff before setting!
        container.setProp(x); // you get the idea
    } else {
        // well we must have a 'container' to set a prop,
        // if we don't then caller must want to read.
        return screen.get(x);
    }
}

If this strategy doesn't mitigate the issue or if you think I didn't understand question properly, then please do attempt to make the case clearer and get us closer to the aim.