Elderflowers are from an Elder tree, they grow in the 'wild', so not really a garden tree. They can grow to about 10 meters or so. There is a more garden friendly variety called Sambucus Nigra, this has black/purpelish leaves, and the flower is slightly darker than the elderflower used for the above recipes. The Sambucus Nigra is chopped down low each year to encourage the dark coloured leaves, as these are appreciated more for their floral/flower arrangement qualities.
I gather elderflowers as I go walking, when I see the blossom appearing, and low enough for me to pick. There are companies that make elderflower drinks commercially here in the UK, they tend to have a lot of elder trees locally, and equipment to reach the higher blossoms.