When you securely have a job that you are happy with and enjoy, inform your previous boss of the new position and resign. You can also try and use your new job as leverage to get your boss to pay you more, but seeing as how you don't like working there, I'm assuming you probably don't really wanna do that.
But you definitely shouldn't just "stop showing up". Even if you don't like your boss, as a respectful citizen it's only proper that you inform them you're not going to be working there anymore. It's just common courtesy. Not to mention if you just stop showing up, your boss is gonna call you over and over anyway to find out what the hell is going on. And so in the end you'll end up talking to him/her, anyway...so you might as well do it in a polite and respectful manner by going up to him/her one day and explaining what's going on.
Also, if you get fired for "not showing up for work", it can make it very difficult to get a job in the future. However, if you quit because you "got a better job", it won't look so bad.
Other companies like to know your previous employment history and figure out why you lost your last job, as well as why there was an employment gap between your two jobs.
You should also inform your boss just because future employers may want to call them as a reference to see what kind of an employee you were. It's good to leave on good terms.
But again - don't even consider quitting your current job until you have a new job that you can securely say "belongs to you" and you feel you are happy with it. Who knows - you may not like this job as much as the last one.