Note: it's strongly advised to use Composer. The instruction below is basically what Composer does for you.

• Download archive extension file of needed version from Github
• Open composer.json
• Find PSR-4 autoload section and remember it for e.g. kmit/select2
• Extract files to corresponding folder in vendor folder, like vendor/kmit/select2
• Add following code to vendor/composer/autoload_psr4.php

'kmit\\select2\\' => array($vendorDir . '/kmit/select2'),

• Add following code to vendor/yiisoft/extensions.php:

'kmit/select2'(name of extension from composer.json file of extension) =>
    array (
        'name' => 'kmit/select2',
        'version' => '1.0.0.0',
        'alias' => array (
            '@vendor/kmit/select2'(path of extension folder alias) => $vendorDir . '/kmit/select2' (path of extension folder),
        ),
    ),

Video Tutroial