You are talking about espaliering the plant. There are many geometric shapes created using this methodology. The wiring pattern is very much straightforward and so I'm assuming you are inquiring after how to begin the process of training the plant. I personally haven't encountered a bougainvilla espalier because most bougainvilla eventually form a woody main trunk which doesn't do well to cover a wall. They do well to grow atop a wall and in fact can be used to deter thieves from entering your property. However there are some tips on going about espaliering the plant.

It's a bit of a complex process which may also include grafting or other means to create 'missing' branches. I'm also assuming the wall is south facing which is the best for bougainvillas.

Ideally your plants have 2 leader branches low in the trunk. (if not, use one of the techniques described below) Set it about a couple of feet away from the wall. It will eventually form a thick trunk and so space is good. Select leader branches to train along one direction on the grid (V shape). secure with twine or any garden suited wire twists. Do the crosses using small branches growing out of the main leader branches. Do not cut off the tip of the leaders until you are satisfied by the growth length. Once it 'hits' a corner, you can gently bend the tip to grow in the opposite direction or perhaps if a young branch is forming near the area, you can then cut off the leader branch. The new forming branch can then continue growing following the diamond shape. So there are 2 techniques to use here.

Once the leader tip is cut off, it will concentrate it's nutrition on the younger branches forcing them to grow outwards. Simultaneoulsy, following the grid pattern, train smaller & younger branches on the cross grids. Remove any in between branches. As young branches are still soft, you can manage to bend some branches without breakage, but do so carefully. I find that if you try to train branches after the plant has just been watered, it's branches are stiff and easily breaks. Other techniques you can utilize is forcing new growth by cutting a small knick just directly above a potential leaf bud, thereby ensuring that all nutrition is directed to this specific bud which will become a branch. or sometimes bud grafting becomes necessary if a branch has died. This procedure is something that I would consider more complex although it shouldn't deter you from trying it out.

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If the plant has only 1 firm leader branch as opposed to 2 which is necessary for diamond pattern. you will need to cut that branch low in the trunk and just above 2 potential branches or buds. That will force at least 2 branch growths.

If the plant has more than 2 leader branches, make your selections for the initial V form and remove the extra branches.

Ianna

The new homes in my neighborhood have bouganvillea espaliered on the front and it looks very nice. (Naples FL)
I agree that boug. has a woody stem and I have seen older installations where the stem is essentially a trunk and most of the blooms are well above head level.
Have you tried a google search? I did one a while back and found a wire espalier but don't remember where now. It involved a glue mounted wire and guide system for wall use.