There are two ways to do this:
The Easy way: gently pick up the vine and weave it in and out of the fence panel gaps, wrapping the curling tendrils about the cross wires. The tendrils are those little thin curly bits that shoot off the stem.
The fun way:
Cucumber tendrils are thigmonastic. Like a Venus flytrap, although not as fast, they move when touched or disturbed. (To read more, check out Wikipedia.)
First choose a vine to be trained with a nice long tendril.