Bobbin lace, as opposed to needle or tape lace, refers to the way the lace is made: a pillow anchors the pattern onto which the twisting threads produced by a cluster of bobbins will be secured with pins. Complicated as the assembly may look, bobbins essentially have just two movements: twisting, and crossing.
Cloth Stitch & Twist
Working with four bobbins, create a cloth stitch, named because it creates the look of woven cloth. Swap the middle two bobbins, left over right; then swap the outer pairs, right over left; then swap the new middle bobbins, left over right. To add a twist, take the left pair of bobbins after completing a cloth stitch and twist them; also twist the right pair. You can do these twists simultaneously, with both hands.
A technique used in English Maltese lace, a picot is a loop around a pin, which gives a lacy edge effect. Use just one pair of bobbins. Twist them several times, then loop the left thread around a pin toward its point and push it into the pattern; loop the other thread similarly, but do so toward the head of the pin. Pull the twisted part through gently, then twist the bobbins.
Some lacemaking techniques do not involve tightening thread around a pin, such as the tally. The result is a block of tightly woven threads, but the bobbins are treated individually rather than as pairs. Separate one of four bobbins from the rest so that the other three hang straight down. Weave the separated bobbin through the other three, then back again, keeping it horizontal so as not to lose the shape. Then, tighten the rows. Tallies can be used to make flower patterns.
The next two techniques are examples of Bucks Point lace designs, which uses a grid with lines of holes running at 60 degrees to the vertical; the honeycomb stitch is used in the honeycomb net, or a pattern of hexagonal holes. To create the honeycomb stitch, work four bobbins in a half stitch (in which one of the bobbin pairs is not switched) and twist; add a pin in the middle; do another half stitch to cover the pin; end by twisting both pairs again. The result will be a visible hole where the pin was.
Gimp is simply a thicker outlining thread that is held together by crossing pairs of threads. Using three bobbins, twist the two inner threads, pass the thicker thread between the two thinner threads, then twist the two inner threads again.