How can I encrypt/decrypt arbitrary binary files using Javascript in the browser?

Note: I won't explain how to decrypt the data, but that should be rather easy to figure out using the code for encryption and the documentation-links provided.

First of all, the user has to be able to select a file via an input element.

<input type="file" id="file-upload" onchange="processFile(event)">

You can then load the content of the file using the HTML5 FileReader API

function processFile(evt) {
    var file = evt.target.files[0],
        reader = new FileReader();

    reader.onload = function(e) {
        var data = e.target.result;

        // to be continued...
    }

    reader.readAsArrayBuffer(file);   
}

Encrypt the acquired data using the WebCrypto API.
If you don't want to randomly generate the key use crypto.subtle.deriveKey to create a key, for example, from a password that the user entered.

// [...]
var iv = crypto.getRandomValues(new Uint8Array(16)); // Generate a 16 byte long initialization vector

crypto.subtle.generateKey({ 'name': 'AES-CBC', 'length': 256 ]}, false, [ 'encrypt', 'decrypt' ])
    .then(key => crypto.subtle.encrypt({ 'name': 'AES-CBC', iv }, key, data))
    .then(encrypted => { /* ... */ });

Now you can send your encrypted data to the server (e.g. with AJAX). Obviously you will also have to somehow store the Initialization Vector to later successfully decrypt everything.

Here is a little example which alerts the length of the encrypted data.

Note: If it says Only secure origins are allowed, reload the page with https and try the sample again (This is a restriction of the WebCrypto API): HTTPS-Link

function processFile(evt) {
    var file = evt.target.files[0],
        reader = new FileReader();

    reader.onload = function(e) {
        var data = e.target.result,
            iv = crypto.getRandomValues(new Uint8Array(16));
      
        crypto.subtle.generateKey({ 'name': 'AES-CBC', 'length': 256 }, false, ['encrypt', 'decrypt'])
            .then(key => crypto.subtle.encrypt({ 'name': 'AES-CBC', iv }, key, data) )
            .then(encrypted => {
                console.log(encrypted);
                alert('The encrypted data is ' + encrypted.byteLength + ' bytes long'); // encrypted is an ArrayBuffer
            })
            .catch(console.error);
    }

    reader.readAsArrayBuffer(file);   
}

<input type="file" id="file-upload" onchange="processFile(event)">

See https://github.com/meixler/web-browser-based-file-encryption-decryption for an example showing encryption/decryption of arbitrary binary files using Javascript in the web browser, based on the Web Crypto API.