How do I save the game?

It can't be done. You can trigger an autosave by finishing a level or buying an item, though.

Don't worry about it - many games that use an autosave feature give a warning like this, even if it's just saved the game. You can read it as 'make sure you hit a checkpoint before you quit, otherwise you'll lose everything you've done since the last one'.

As long as you quit after hitting a checkpoint your progress will be saved.

Go to the bar in the start of a new game and you can create a new autosave under the character option. You can visit bars within the game to save at anytime...