What's it look like?
You'll notice little transparent squiggles on leaves that are attacked by leaf miners. 
Sometimes young shoots and leaves are twisted and deformed as a result.

What they attack:
Miners attack a variety of plants including citrus, beetroot, nasturtium, potatoes, beans and many more.

What to do before it arrives:
Leaf miners are insects that lay their eggs on leaves of plants and the larvae chews (or tunnels) its way through the leaf leaving silvery trails behind.
So one way to avoid the problem is to stop the insect from parking on your plants and laying their eggs.  Do this by spraying the foliage with white oil or new certified organic botanical oil called 'eco-oil'.  This makes the leaves slippery and the insect is less able to land on them.

What to do if you already have problems:
Just cut off the affected part of the plant or leave it if you can tolerate it.
By the time you notice it the larvae will already have hatched into its adult stage and flown away.