The most typical use of twine on a bicycle, is to secure the inner edges of handlebar tape. Normally, bar tape is secured with black electrical tape and left as is, but I find that this looks unfinished. With twine, the handlebars will look more appealing and the tape will be more securely attached.
I use cooking twine, which is softer to the touch than industrial twine. It is white in its untreated state and turns caramel-brown when amber shellac is applied.
After wrapping your bar tape and securing the inner edges with electrical tape, the twining can begin.
First apply a layer of clear double-sided tape over the electrical tape.
Cut a half-armlength of twine.
Apply the twine over the double-sided tape by simply wrapping it around the handlebar and placing it down neatly onto the sticky surface of the tape. There should be no gaps and no overlap.
When the surface of the double-sided tape is covered with twine, cut the remainder off. There is no need to secure the twine, since it is stuck to the double-sided tape. This will provide a good temporary hold until shellac is applied.
Using a paintbrush or a sponge brush, cover the twined area with amber shellac following the same principles described here.
After three layers of shellac, the twine should feel completely solid and have a deep amber colour to it, at which point the project is finished. Your bar tape will be more secure than ever and will look great.
If you've finished twining your bars and still crave more, do not despair: There are lots of other places on a bicycle where twine can be used. I twined the chrome connector piece between the rack and the rear stays on my Pashley, because I was not satisfied with how the expanse of chrome stood out in an otherwise green and black colour-scheme. The dark amber twine softened that area up, and integrated it nicely with the wicker basket, brown leather saddle, and handlebar grips.
Here is a close-up of the twined rack connector. I thought that this was a failry subtle detail, but to my surprise, several people commented on it while examining my bicycle.
My most daring use of twine thus far, has been the twining of my Shimano Nexus shifter. My reasons for doing this were two-fold: I thought that the big rubber shifter was too modern for the aesthetic of the Pashley's handlebars, and I also found it unpleasant to the touch, especially in the sumemr heat. Covered with shellacked twine, the shifter blends in better and is more comfortable for me to use, as the twine provides a better grip than the rubber. There was some concern regarding whether the twine would adhere well to the rubber, but this was not an issue; just wrap it tightly prior to shellacking.
Of course, once you do this to your shifter, there is no going back: the shellac will disfigure the rubber if you ever decide to remove the twine and you will need to buy a new one. Twine at your own risk!
For more twining ideas, Rivendell has some nice pictures and instructions, as well as hemp twine for sale. Also have a look at this marvelous twined water-bottle pictured on The Epicurean Cyclist.