Hi Anniina,
Big question! So first thing is the brace or guy (I presume that you are UK based) is just the windward "sheet", so if you think of it in these terms then it does become easier. The guy is only used on the windward side of the boat. Why have this extra line? on the 31 footer the spinnaker is a lot smaller and the loads are not as high. The spinnaker pole can therefore easily be pushed out on the sheet (which becomes the guy) when end for end gybe.
Increase size to the 40 and the loads on the pole become greater. During the gybe with sheets and braces/guy, the guy is not under any load. This enables the pole to be changed from the working guy to the new working guy. When the pole is detached from the guy during the gybe the spinnaker if flown using the sheets as you would have done previously. One feature that is needed to enable the dip pole gybe is a beak that locks open. this ensures that the old working guy will fly out of the pole clip.
So the blow by blow process is something like this.
Set up, 1 crew (bowman) at front of boat with the "lazy guy" ready to place into the pole end. 1 crew to "trip" the pole or release the working guy from the pole (this could be the bowman). 1 person to lower and raise the pole topping lift, 1 person to trim both spinnaker sheets, steering and gybe mainsail. Move the mast end of the pole up the mast to allow the pole to swing through the foredeck
Step 1; run square and trim pole back. Ease spinnaker sheet. Take up windward spinnaker sheet.
Step 2; trip the pole to release the guy from the end of the pole. The spinnaker is now flying on the two sheets, release the old guy from the winch.
Step 3; Bowman Pulls the pole into the front of the boat, and the pole topping lift is eased to allow the tip of the pole to swing through to the other side of the boat.
Step 4; the main sail can be gybed, note that the spinnaker is still being flown on both sheets.
Step 5; (can happen as main is gybed) bowman places new brace in the pole beak and calls MADE or other call to advise the pole is ready to be lifted to the working position. Once the new guy is in the beak the bowman pushes the pole out and up. The pole topper is pulled on to lift the pole to the spinnaker and the new guy is placed on the winch and trimmed on to position the pole. The windward spinnaker sheet can be eased.
Step 6 High fives!
Good luck