Wood – How to attach two pieces of wood in an invisible way

I don't know if there's something for screws in wood, as wood's a rather strange material.

For bolts into steel, however, there's the AISC Manual (no prices listed, but expect it to be in the $300+ range); there used to be a separate book on joints, so you could calculate the strength based on the size of the fastener, bolt pattern, etc. There was also a section for calculating the strength of different weld patterns.

Now, the rules for the optimal strengthy are going to be similar -- further apart will support a greater moment, so when the contact patch is a square, you want the first two to be in opposing corners. If using four, fill all of the corners. However, because it's wood, you have a chance of spliting, so you don't want to go too close to the edges. (if you have to; pre-drill).

The other thing to remember is that with screws and bolts, the fasteners shouldn't be taking the full load -- they're pulling the structural material together, so that the load's transfered as friction ... this means if you see a gap between the two pieces, you need more fasteners. If you have a really large contact patch, drop another screw in the middle.

You call it a patio, so I assume it is not a wood deck (which would be easier to add a railing). I'd avoid attaching it to the house though it seems that the other end of the patio roof may be tied to the house already. Consider driving a super spike into the ground at each end to hold a post that will be the ends of the railing. At a 10 foot span, you'll want one in the center of those two as well. If driving the spike just off the patio won't work, then remove a patio stone and drive the spike where you need it. You can break/ cut the patio stone to fit around the post once its in place.