The 1st thing to do is make lots and lots of eyelets. I have to take some pics of this part of the process but you will get the idea of they look from the right pic in the 2nd row.  Make a small wire hook and chuck it in a Dremel.  Loop a short length of .006" fly tying wire  on the hook and at a low speed twist the wire tight.  The doubled eyelets are made by taking a piece of wire to make an eyelet and pass it through the hole of 1 already made.  Twist it with the Dremel as before and you'll have 2 connected eyelets. 

If you look at a lot of rigging on the 1:1 birds you will see that a common look is a turnbuckle with eyelet at each end and cables attached to that.  The cable too can have an eyelet that is made by a metal piece to form the loop and the cable is either woven back into itself or whipped with a thin wire.  The photos below start at the point of simulating that whipped look at the cable end.

Glue one of the lines made previously into a pre-drilled hole.  I have seen many biplane builds with the top wings on and a nest of lines curled up glued in place in preparation for the final rigging.  If this is thought out carefully and the cables that are more toward the "inside", you should be able to get the outer ones in without too much trouble.

Glue an eyelet for the other end of the cable in place.  All the holes for rigging should be pre-drilled.  Drilling at an angle can be tricky so don't bother.  Drill the holes straight.  When the eyelets are glued in place they can be easily bent to at an angle if appropriate.

The barrel of the turnbuckle is a 1/8" (that scales up to 4"... perfect) length of 0.5mm brass tube.  If need be the end of the tube can be widened a bit by poking a straight pin into the ends of the tube and giving it a little wiggle.  If the eyelets are twisted tight they should fit in the tube.  Glue an eyelet with the line at one end and a doubled eyelet at the other.  Use slow curing CA because capillary action will pull the glue through the tube and it hardens too quickly you will never get the other side in the tube.

A drop of thin CA will keep it from unraveling.  Trim the excess off with a very sharp blade.

... then back though the tube in the opposite direction.  That's important to keep part right or the tube won't slide back up the line.

I use some small tweezers to grab the tube and slide it up to the eyelet keeping tension on the loose end of the line.  Once it's snugged up at the tension I want I hold the end of the line at a little bit of an angle to keep the tube from sliding back down.

Slip the rigging line through a piece of brass tubing and slide it down out of the way a bit.  Open the end of tube as described above if need be and they can be, very carefully, drilled out a little to make some room.  In this case I am using a multi-strand fly tying thread that when pulled tight has a pretty even look for thickness down its length.  I take about 1' on the end and run it trough a drop of thin CA and let that harden.  It doesn't take long.  This stiffens the thread and I cut the tip at an angle to aid in threading it through the tube.

Feed the line through the open eyelet...

And there you have it.  Nice tight rigging.  This does add some stability to the models and it is important to get the tension even form side to side or it can pull the wings out of alignment.  Do the same cable on each side before moving on to the next position.  Depending on what material you use you may even be able to use the blown out match trick, like for stretched sprue, to get the line a bit tighter if need be.

A little drop of thin CA to soak up into the tube, let that harden, here i am touching it with a little accelerator to hurried it along, and trim with a sharp blade.  I find a scalpel really cuts best in this situation.

Count how many rigging line you are going to need and make them all first.  Clamp an eyelet in a forceps or something that will hold it secure.   I take a length of whatever line I am using about 15" long when the rigging will at most be about 6" long when done.  This length give me enough to work with to tie the 1st know and for the final connection.  Tie the line to the eyelet using a clinch knot.  A google search will get you a diagram of how it ties.  Easy knot to make and when done looks like that whipped cable look I am going for.