The push button is just that, when you pull the handle back then press the push depress the button with the spring on it that will hold the caliper handle back keeping bike in neutral for idling the engine.
The barrel adjustment where the cable goes should be turned all the way in when attaching the clutch cable to the engine. Pull out all you slack while doing this then what ever clack is left can be fixed by that barrel adjustment.
FYI these clutch hand calipers are some times cheesy and brake. This is easily remedied by putting a regular brake hand caliper there. Sometimes you can find one with a longer handle making the clutch easier to disengage . longer handle = more leverage
let us know what you find. Post pict if need be. Feel free to ask questions. There are no dumb questions here! Welcome to the forum Demon.