Squirt a few ounces of RealLemon juice or fresh lemon juice into the other tray or bowl or what-have-you.  It's better if it's white so the bugs can be clearly seen in the lemon water.  However, they'll show up well enough in the shiny aluminum tray.

Fill up the container with fresh water (but not running).  The profusion of bubbles means there's enough lemon juice in the water, and you can't have too much.

Here, we'll show how to clean romaine lettuce since it is so common, and commonly used in our kitchens.  After discarding the ragged outer leaves if you're not using hearts of romaine, cut off the stalk end.

Immerse in the lemon water and separate the leaves.  This can be quite an operation for tightly wrapped vegetables like cabbage which has to be chopped, cored, and soaked for quite a while before the leaves begin to come apart.  Make sure all the leaves are fully separated and completely immersed.

Swish each leaf in the lemon water, remove, and place in the (preferrably running) fresh water adjacent.  When all the leaves have been removed, examine the empty pan of lemon water for bugs.  They hate the lemon juice and once immersed they know it's time to get off the bus.  Which is exactly the message we want to send them.  If you've found bugs, you'll have to do it again until you don't find any.  Scoop out the bugs before re-immersing, although a running water rinse will keep them from re-attaching themselves.  The usual rule (chezaka) is 3 out of 10.  However you're checking, leaf by leaf or bunch by bunch, if 3 are clean you can assume the next 7 are as well.  If you do find more than a few bugs and you're doing a bunch at a time, change to a leaf by leaf procedure.

Here comes the checking part.  Using a strong, diffuse light source (an old x-ray film viewer is perfect), hold each leaf against the light and check for anything that doesn't look like a leaf.  The clinging insects will rarely be found, but some burrow into the stalks and appear as little brown discolorations.  Dig them out with a knife or discard the whole leaf if you've mutilated it by doing so.  If you found any bad stuff, send it through the washing process all over again.