I’m assuming from your post that you already have a copy of ASTM B 117-3, which has pretty good “functional” schematic diagrams of typical cabinet construction (Figures X1.1 thru X1.3). There's also an un-annotated schematic at
. The saturation/humidification tower (on the right hand side at the above site; Item 3 of the B 117 schematic) bubbles air through a heated column of water. This humidified (saturated) air is piped to the atomization tower (inside the cabinet on the left of the diagram at the above site & Item 12A of the B 117 schematic) that uses this air to draw to draw the neutral salt solution from a reservoir (via a venturi spray nozzle) to produce the salt "fog."
These things (even when manufactured by companies that do it for a living) can be persnickety to get "balanced" to the B117 specification requirements (temperature, collection rate, pH, specific gravity, etc.). If you want to put much weight in your test results (as much as appropriate for this test method, that is) I really don't see this as a do-it-yourself project, and you're likely to find yourself spending more piecing one together than if you purchased one outright.
Some options:
1) Farm out your salt spray tests to a contract test lab with a cabinet. (This may be the most practical and economical if your requirements are less than constant).
2) Buy a good used cabinet (and make sure you get the manual). Add some time in your schedule to get it up running and stabilized. See if you can a commitment from whoever is selling you the cabinet to give you a hand setting it up and getting it properly stabilized.
3) If you really want to try and build one, good luck (really). You may want to consider purchasing at least some key components (e.g. atomizer venturi). Sizing of the cabinet and components is important. If you buy a atomizer nozzle, make your cabinet interior dimensions roughly the same as the cabinet the nozzle is supplied/designed for. I note the link I supplied above has a "(Detailed Schematic Available Upon Request)" statement. You may want to request one (but may not want to bring up that your interest is in building your own). Don't expect, however, any support in getting your "homebrew" up and running. I do think you run the risk of spending what budget you do have and ending up with a chamber that won't meet B117 requirements (if that's what your requirement is).