I fly the 777 only (Moving over to the A359 when it comes out). I will use this Document for future reference. Make sure your autopilot is on first before you hit the APPR.
Using that document, let’s assume that you’re vectored in on 20R, at 4000ft, on a heading of 270, east of NYLON, and you are around 3nm from the localiser interception point. Once you received the final message of “[callsign], Turn left heading 240, Maintain 3000 until established on the localiser, cleared ILS Rwy 20R approach”. Your aircraft should maintain the altitude that it currently is at, or will descend to that altitude and hold. In this case, your aircraft will turn to 240 and descend to 3000ft. Set your V/S speed to whatever you please and let the aircraft descend [I will set -1000ft in this case]. After replying the radio call, I will press APPR (your aircraft should still be descending at this point). The aircraft will maintain descend and maintain 3000ft and then capture the localiser. At this point, let the computer do the work but monitor it. When the moving line hits the box before the vertical line that doesn’t move (in this case, the line will come from the right, moving to the left), the aircraft will turn towards the runway. At this point, the rectangle box next to the altitude meter should show that something is blinking. Let the aircraft fly and correct itself to the correct heading. Then, at some point, that thing stops blinking and it starts to come down. At that time, the computer registers the aircraft as having captured the glideslope. Once it has passed the centre of the vertical rectangle next to the altitude meter, the aircraft will descend automatically showing that the autopilot has captured the glideslope. From there, the autopilot will guide the aircraft down to the runway. At this time, no matter how much you change the altitude, it will not follow the commands input into the autopilot. From there, you need not worry about your V/S. Leave the A/P on as disengaging it will put the aircraft back under manual control and will take inputs from your calibrated setting. From here, let the aircraft descend to an altitude that you are comfortable with and then (I cannot stress this enough) CALIBRATE YOUR DEVICE, THEN disengage the APPR (or AP) before taking it to touchdown. Do remember that pressing APPR will only disengage the ALT, VS and Heading settings. it WILL NOT disengage the autothrottle. So if you are worried of a stall, and you want to let something else handle the speed for you, leave the autothrottle on, but remember to disengage the autothrottle BEFORE flaring the aircraft to touchdown because failure to do so will result in the aircraft throttling up during the flare and forcing you to do a go-around, or even resulting in a stall may set the aircraft down resulting in a heavy landing that even forces the oxygen masks to drop in the cabin.
Hope it helps