There is a full set of instructions for this in the watering box when you hover your mouse over a fully grown Bamboo plant in your own garden.  It's clear, though, that this still causes some confusion so I thought it would be useful to have the information contained together.   I've updated it so that it should address other questions which arise about the Giant Panda too and I'll ask the mods to remove the original thread.

1.  You must have a fully grown Bamboo plant in your garden.  To plant the bamboo, buy a bamboo pot from the pot shop and hover your mouse over it.  The only option should be to plant bamboo.  If you can't see that as an option, go to the Bonus Seeds section of the seed shop.

2.  You must also have an empty plate.  Make sure that the plate is completely cleared, not just empty, otherwise the bamboo food has nowhere to go.

3. To get the bamboo food onto the empty plate, you need to spot black and white wildlife in other gardens (for example, Panda, Badger, Skunk, Raccoon, Penguin, Magpie, etc).  The garden you spot the wildlife in must also have a fully grown bamboo.

4.  If you spot a Panda but the bamboo has become RTH since the Panda was programmed in, you will get the Panda but not the bamboo.

5.  Pandas give double organic food (10 feedings).  Any other black and white wildlife gives organic (five feedings).

Additional information:

The bamboo will remain fully grown for 24 hours.
The more bamboo plants you have in your garden, the better the attraction for the Giant Panda.

List of Black and White wildlife:

Badger & Babies & Family
King Penguin (both land and underwater)
Magpie and Pairs of Magpies
Panda
Puffin (both land and Underwater)
Raccoon & Baby & Family
Skunk
Zebra & Baby & Family
Zebrafish

Can I wait until I have spotted a Panda in another garden before I plant bamboo in mine?  Or will it not put bamboo on my empty plate if I haven't any growing in my garden? 

As per point 1, above, you have to have a fully grown bamboo in your garden to get the food on the empty table.

Thank you, Tracy, wasn't sure if only needed to attract Pandas to the bamboo on the table just :)

I suppose it needs to be fully grown as well before a spotted panda will leave me bamboo on my plate?

Yes.

I finally spotted a Giant Panda and got bamboo on the plate in my garden.  However, the bamboo plant in my garden will be RFH in less than an hour.  Will the bamboo on the plate still attract or should I get another bamboo planted fast to still be able to attract?  Thanks!

This is probably too late but you need to replant.  The bamboo will only attract the Panda when fully grown.

Just a little bump as so many people seem to be having problems with this again :)

I thought it might be useful to list the attractants for the Red Panda and Gorilla, since they also feed on Bamboo, and need the fully grown Bamboo plant in the garden too.  I'll include them in the first post when I next update this.

Red Panda:  fully grown Bamboo, fully grown red Bellis Lycaena and fully grown red Piscis Aquebullae (you may need to use sparkle dust the change the colour).  Bamboo food needed.

Gorilla:  fully grown Bamboo, fully grown Fructus Odonata and fully grown Aureus Primus.  Bamboo food needed.