The following example encrypts a given data block using AES. The encryption key is derived in a secure way (random salt, 1000 rounds of SHA-256). The encryption uses AES in CBC mode with random IV.

Note that the data stored in the class EncryptedData (salt, iv, and encryptedData) can be concatenated to a single byte array. You can then save the data or transmit it to the recipient.

private static final int SALT_BYTES = 8;
private static final int PBK_ITERATIONS = 1000;
private static final String ENCRYPTION_ALGORITHM = "AES/CBC/PKCS5Padding";
private static final String PBE_ALGORITHM = "PBEwithSHA256and128BITAES-CBC-BC";

private EncryptedData encrypt(String password, byte[] data) throws NoSuchPaddingException, NoSuchAlgorithmException, InvalidKeySpecException, InvalidKeyException, BadPaddingException, IllegalBlockSizeException, InvalidAlgorithmParameterException {
    EncryptedData encData = new EncryptedData();
    SecureRandom rnd = new SecureRandom();
    encData.salt = new byte[SALT_BYTES];
    encData.iv = new byte[16]; // AES block size
    rnd.nextBytes(encData.salt);
    rnd.nextBytes(encData.iv);

    PBEKeySpec keySpec = new PBEKeySpec(password.toCharArray(), encData.salt, PBK_ITERATIONS);
    SecretKeyFactory secretKeyFactory = SecretKeyFactory.getInstance(PBE_ALGORITHM);
    Key key = secretKeyFactory.generateSecret(keySpec);
    Cipher cipher = Cipher.getInstance(ENCRYPTION_ALGORITHM);
    IvParameterSpec ivSpec = new IvParameterSpec(encData.iv);
    cipher.init(Cipher.ENCRYPT_MODE, key, ivSpec);
    encData.encryptedData = cipher.doFinal(data);
    return encData;
}

private byte[] decrypt(String password, byte[] salt, byte[] iv, byte[] encryptedData) throws NoSuchAlgorithmException, InvalidKeySpecException, NoSuchPaddingException, InvalidKeyException, BadPaddingException, IllegalBlockSizeException, InvalidAlgorithmParameterException {
    PBEKeySpec keySpec = new PBEKeySpec(password.toCharArray(), salt, PBK_ITERATIONS);
    SecretKeyFactory secretKeyFactory = SecretKeyFactory.getInstance(PBE_ALGORITHM);
    Key key = secretKeyFactory.generateSecret(keySpec);
    Cipher cipher = Cipher.getInstance("AES/CBC/PKCS5Padding");
    IvParameterSpec ivSpec = new IvParameterSpec(iv);
    cipher.init(Cipher.DECRYPT_MODE, key, ivSpec);
    return cipher.doFinal(encryptedData);
}

private static class EncryptedData {
    public byte[] salt;
    public byte[] iv;
    public byte[] encryptedData;
}

The following example code shows how to test encryption and decryption:

try {
    String password = "test12345";
    byte[] data = "plaintext11223344556677889900".getBytes("UTF-8");
    EncryptedData encData = encrypt(password, data);
    byte[] decryptedData = decrypt(password, encData.salt, encData.iv, encData.encryptedData);
    String decDataAsString = new String(decryptedData, "UTF-8");
    Toast.makeText(this, decDataAsString, Toast.LENGTH_LONG).show();
} catch (Exception e) {
    e.printStackTrace();
}