As some background from what I've been able to determine, these high performance lines are all made from what is called gel-spun high density polyethylene. Honeywell is the manufacturer in the US. Dyneema is the major manufacturer in Europe. I believe they are the only two suppliers because it is a patented, licensed technology.
In various informal tests the Spectra lines are much less likely to get damaged in ordinary handling and stand up much better to use. They are available, as fishing line, in many different diameters and strength ratings. All of the brands I've tested can be made into useable lines simply by tying a loop with an overhand knot. The strength is very uniformly half, or slightly less, of the rated strength. The lines break either at the knot, or a couple inches away. According to the kite flyers, there are various techniques, such as putting a sleeve of other material over the line, and possibly using certain types of knots, that will get a higher breaking strength.
Just for comparison purposes, .018 stainless steel lines break at almost exactly 50 lb. pull. They always break at the termination, whether it is wrapped, or crimped, or they break at a previously kinked spot in the middle of the lines. 100 lb. Spectra fishing line(Power Pro brand), has a diameter of about .0181 in.(it's a bit hard to measure exactly since the line is soft). With simple knot terminations it breaks at 45-47 lb. The Spectra weighs around 5 gr. for a 52.25 ft. set, 018 steel weighs 31 gr.
In a couple simple abrasion tests, hanging a 15 lb weight from line and rubbing across it with another line stretched to 10 lb. or so on a bow, the 100 lb Spectra held up to 200 1 ft. strokes. 018 Stainless steel held up to 50 strokes under similar test conditions. We've done quite a bit of combat flying using 30 lb. Spectra, which is the same strength as .012 steel lines. The steel lines broke/kinked/tangled at about 10 times the rate of the Spectra lines. In about 30 matches none of the Spectra lines were damaged, but 3 sets of steel lines were either broken, kinked, or otherwise damaged in line tangles. However, when I ran the abrasion test above, using steel wire on the bow against the Spectra line, the Spectra only held up for 10 or so strokes, which is at odds with the flying tests.
Bottom line is that you can use the same diameter Spectra as stainless steel line. Figure the fishing line will break at half the rated strength. Major brands are Tuf-Line, Power Pro, and Spiderwire.
Line diameter conversions:
15 lb TUF- Line XP = 4 lb mono
20 lb TUF- Line XP = 6 lb mono
30 lb TUF- Line XP = 8 lb mono= .26mm=.010 in.
50 lb TUF- Line XP = 12 lb mono= .31mm=.012in 25 lb. in stainless
65 lb TUF- Line XP = 16 lb mono= .37 mm= .014 in.
80 lb TUF- Line XP = 18 lb mono=.38 mm= .0153 in 40 lb. in stainless
100 lb TUF- Line XP = 20 lb mono= .40 mm=.0157in.
130 lb TUF- Line XP = 30 lb mono= .52 nn= .020 in. .018 stainless breaks at about 50 lb.
150 lb TUF- Line XP = 40 lb mono
200 lb TUF- Line XP = 50 lb mono
the diameters vary slightly from manufacturer to manufacturer. These mono diameters came from Momoi.
Terminations:
The easiest is to fold the line over and tie a double overhand knot in it- make an overhand knot and then wrap the line through a second time. Spit on it and pull on the loop to work it down into a smooth knot. The double overhand knot is a bit stronger than a single overhand knot.
The other way is to tie the line to a clip using a blood knot. Look it up on google, it is too hard to describe, but not hard to do.
I've also tried using a crimp tube, eyelet, and a short piece of plastic wire insulation. This is looking very promising but will take some more testing. Using two pieces of plastic tubing over the line and then putting both of them in the crimp seems to be the best way. The free end of the line has to be tied into a mulitiwrap stop knot, otherwise the Spectra will just slide right out no matter how you crimp it. This termination looks like it will hit 70-75% of the rated breaking strength.