First, there is the waiting - that is the bit where the adults are putting on the lights! Our pre-schooler found this very difficult as he was very excited to be involved in decorating the tree.
Then the decorations, these hold several different learning opportunities, you can label the items - tinsel, baubles, beads and the ornaments - snowmen, angels, Father Christmas, reindeer. You can practice colours and shapes (depending on your decorations!). You can practice prepositions / adjectives / opposites - on the tree 'v' off the tree, high 'v' low, top 'v' bottom, put it next to the star / above the snowman / below the bauble / under the tree.
Lastly there is the big lesson of not touching the finished tree! Our toddler is still learning this one so I keep being presented with the baubles with him saying 'ball'.