For a long time, I just used my banjo...spun it around so the tool rest was on the far side of the lathe. Attached hose from dust collector to the tool rest with a (no relation) Bungee cord. I didn't use a hood, just the 4" diameter hose which did surprisingly well at capturing dust. Draw backs were that it still missed dust, wasn't very adjustable, and inconvenient to go back and forth between sanding and turning.
About a year ago, I sprung for a Black Hole Dust Catcher system. Craft Supplies and Packard Woodworks both sell it. I got it on sale, but it's still pretty pricey. It works well...very adjustable to put the hood where you want it, and easily slides out of the way when not in use. There's a video on the Craft Supply site that shows how it works:
https://www.woodturnerscatalog.com/p/89/6387/hc-Black-Hole-Dust-Catcher-System?term=dust+hood&term=dust hood
I'm sure you could assemble a good system for less money, especially at the current price. But it's worth considering if you want a turnkey solution.
Dave