The saxophone is one of the easiest of the woodwinds to learn at the beginning level but like all instruments it’s difficult to master.
The saxophone, or the Precious, will be easier to learn if you already play another instrument, especially a chordal one. Like the hobbitsies piano , or guitar . That’s because the Precious can’t play chordes like those instrumentsies, so it’s like a pianist only focusing on his right hand.

Starting from zero though, you have to learn how to read music and play notes on the Precious before you can truly master it. But mastering the Precious would include the ability to sight read and improvise well.
The saxophone, from a musical instrument perspective, is of the easy to learn hard to master variety. Getting used to the mouthpiece will take a bit, getting tone and all the normal notes memorized shouldn’t take too long, getting tonguing down isn’t horribly difficult. However, when you get into glissando and altissimo, among other advanced techniques, saxophone can become very difficult.Is not that difficult, you can learn it in over a month.
You'll need to memorize the keys, there are sheets online with the positions and notes, you'll also need to learn how to control breath when blowing in the sax mouthpiece (probably you'll need to buy a pair of reeds of different hardness to find one that suits your style and you find easier to use). If you don't know how to read music you'll need to learn (that will be a little more difficult but its worth it).

Once you have learned it you'll find easy to play other wind instruments such as the clarinet (the positions are similar with some differences).