Jim Thompson wrote:
Thompson's Honey-Do project of the Day...

http://analog-innovations.com/SED/WireBasketAndRail.jpg

I need a clever way to attach wire basket to under-rail drawer glide.

...Jim Thompson

If it's truly what they call under-rail, that means the rail is
beneath the basket. Mount the rails to a piece of plywood cut to
fit the opening. Gives you a sliding shelf to set the basket on.
Affix the basket to the shelf by whatever means you like.

If I've got it wrong, and it is really rails that are top mounted,
here's some possibilities below:

Looks like the "lip" at the top of the basket is about 1/2".
So route or (table saw) a 1/2" deep slot in 2 pieces of 3/4" stock,
each piece the length of the "lip". The "lip" slips into
the slots - the rails mount on the outside of the stock.
Like this:

--- ---
R| | | |R
A| --- --- |A
I| |\ /| |I
L| || || |L
--- | | ---
| BASKET |
| |
|__________|


You may need to drill a hole down from the top of the stock
through the basket lip so you can screw or dowel (finishing
nail dropped, not driven, into the drilled hole). One at the
front and one at the rear on each side. The above solution
requires a width equal to the basket + 1/2" for the stock
plus whatever the rails need.

If you have more width, you could just build a rectangle into
which the basket fits nicely, mount the rails on the long
legs of the rectangle and install the basket. Then slip the
rails into the corresponding mechanism.

If you have no extra width, cut the stock to fit inside the basket
and screw the rails to the stock from the outside. If you go that
route, round over the edges of the wood so that hands inserted into
the basket have no sharp corners to hit. There's no need for slots
in the stock, but you do want to make sure that the "sandwich" made
by the stock, basket and rail can't move once assembled.

Ed