I want to build a desk tabletop with the surface being maple, but 8/4 maple was quite expensive so I'm opting for half the thickness. However, this narrows down the options for joining the boards to make the surface. What method should I use to join these 3/4 wood boards? Is 3/4 thick enough for pocket hole joining to be practical? Preferably the technique should not involve specialized machines or tools.
I'd suggest joining 3/4 maple planks into a table top exactly the same way you'd join 8/4 maple planks. Cut the edges nice and square, joint them to ensure they're 100% flat, then glue them up and apply every clamp you (and everyone in your neighborhood) own. Some gluing cauls will help to ensure it stays nice and flat while you're clamping and the glue is setting.
A jointer would make squaring the edges easier, but this would likely fall into "specialized tools", so you can do it with a jointer's plane. Of course, that may be considered "specialized", too, so you'll have to draw the line somewhere on what's "specialized" vs "how nice do you want your table top to be". If you don't get those edges really square, your glue-up won't be flat, then you'll have to sand or plane it flat and will end up with a less than 3/4" thick surface.
I wouldn't use pocket screws for any of it (even though I just picked up a pocket screw jig a couple of months ago).