private String getTwitterStream(String screenName) {
			String results = null;

			// Step 1: Encode consumer key and secret
			try {
				// URL encode the consumer key and secret
				String urlApiKey = URLEncoder.encode(CONSUMER_KEY, "UTF-8");
				String urlApiSecret = URLEncoder.encode(CONSUMER_SECRET, "UTF-8");

				// Concatenate the encoded consumer key, a colon character, and the
				// encoded consumer secret
				String combined = urlApiKey + ":" + urlApiSecret;

				// Base64 encode the string
				String base64Encoded = Base64.encodeToString(combined.getBytes(), Base64.NO_WRAP);

				// Step 2: Obtain a bearer token
				HttpPost httpPost = new HttpPost(TwitterTokenURL);
				httpPost.setHeader("Authorization", "Basic " + base64Encoded);
				httpPost.setHeader("Content-Type", "application/x-www-form-urlencoded;charset=UTF-8");
				httpPost.setEntity(new StringEntity("grant_type=client_credentials"));
				String rawAuthorization = getResponseBody(httpPost);
				Authenticated auth = jsonToAuthenticated(rawAuthorization);

				// Applications should verify that the value associated with the
				// token_type key of the returned object is bearer
				if (auth != null && auth.token_type.equals("bearer")) {

					// Step 3: Authenticate API requests with bearer token
					HttpGet httpGet = new HttpGet(TwitterStreamURL + screenName);

					// construct a normal HTTPS request and include an Authorization
					// header with the value of Bearer <>
					httpGet.setHeader("Authorization", "Bearer " + auth.access_token);
					httpGet.setHeader("Content-Type", "application/json");
					// update the results with the body of the response
					results = getResponseBody(httpGet);
				}
			} catch (UnsupportedEncodingException ex) {
			} catch (IllegalStateException ex1) {
			}
			return results;
		}

Step 1: Encode consumer key and secret

First, we need to URL encode the consumer key and secret. Java has this function built-in, URLEncoder, be sure to pass your encoding. Then we concatenate the encoded strings with a semi-colon separating them and Base64 encode the whole thing. This is the one spot where I ran into some trouble. I wasn't sure what flag to pass. I initially tried, Base64.DEFAULT, which didn't work. Luckily, there weren't that many options, and when I tried Base64.NO_WRAP, it worked. 

Step 2: Obtain a bearer token