Playing quietly through a sax is all about having a sufficient embouchure (mouth position/tension), to create a sound when pushing less air through.
It's very normal to initially be playing loud when first learning the sax, and your embouchure is less developed - unfortunately this develops mainly through sustained (loud) practice. I wouldn't say there's a particular secret to playing quietly - only exactly what you'd expect - blowing less.
Let's knock out the basics, to ensure you're not making a simple mistake which is making things harder. As a beginner, you should be using a low strength reed (1.5), and a 'basic, no-frills' mouthpiece. (You probably have one of these, just be aware there are mouthpieces specifically designed to make a big sound, which won't be suitable for learning on - if you've brought second hand.) At the moment, I imagine when you blow less, you make no sound, and if you start to blow harder, you get a bit of a honk.
That unfortunately, is somewhat the nature of learning sax, your mouth adjusts almost 'subconciously' to make things easier for you. Your best way to practice playing quieter I would say is to simple attempt to make a respectable sound be blowing less, and adjusting your mouth to do the hard work, rather than blowing more to get a sound out, as I image you currently would do.
If your problem is practising indoors, "Saxophone mutes" are available. There are simple £25 ones, which involve shoving a few things inside your sax, and more extravagant £400 ones, which essentially are a container for the entire sax. I personally have never tried one, and they have mixed reviews, but you may be interested in taking a look. Don't expect the same results are brass instrument mutes of course, as the sound is formed in an entirely different way!
I would completely recommend getting a couple of lessons to start off with, to make sure you are approaching things in the right way. Embouchure technique is something most definitely best taught by someone who can see what you're doing with the sax, and advise. I respect however, that you've noted this is not an option you're interested in - however I wouldn't want to post my answer without reference to it!