It would be helpful if you had pictures of the clew end of the boom so that we can see the hardware back there.
In a broad general sense, guessing at what is probably at the aft end of the boom, it would seem like there should at least be a cheek block near the end of the boom. The mainsail should have slot in the foot somewhere below the clew reef cringle as well.
Looking at the photos and based on those conjectures, before going sailing I would rig a long line to be used to tie in the reef at the clew. I would start attaching that line by tying an eye in line with a bowline around the boom at the location of the slot in the mainsail, or in the case of a loose footed mainsail, below and aft of the reef clew cringle. Then I would run the line through the reef clew cringle, then aft on the boom to the cheek block (conjecttured above), then forward to the block that you can see near the gooseneck, and then aft again to the cleat on the side of the boom. That line needs to be loose enough that you can raise the sail without the line being tight.
The way that I would rig a reef would be to release the mainsheet, vang, and downhaul and lower the mainsail so the reef tack cringle was approximately at the height of the gooseneck track. I would then tie webbing or a short length of line through the kringle and under the gooseneck and tie them tightly so the cringle is held down tight to the boom at the gooseneck.
Then I would tension the long line for the clew of the sail taking all the slack out of the line so that the clew cringle is pulled down hard against the boom and aft so that the fot of the reefed sail is very tight. If this is a comparatively small mainsail, you should be able to tension it and bring in the reef with the sail flying. On a bigger sail, you do not have the mechical advantage to tension the foot of the sail with the sail flying and so may need to drop the sail so the foot of the sail has no wind in it in order to tie in the reef clew line properly.
Once the clew is tied off, then tension the down haul and vang and go back to sailing normally.
Jeff