Lights. Check they work first. We use two sets of white lights (much to DH's dismay, who would prefer naff coloured ones) and do one from top-to-bottom around the centre of the tree, and then another top-to-bottom going around and around the branches.
Then all the hanging decorations go on. I don't use tinsel (another misery I have wrought upon DH) but I do have some angel hair scattered around. Strings of beads are nice too. I don't use them because cats, but they look nice strung around the tree after the baubles go on.
A lot of my American friends use ribbon on their trees, like this. I've never tried it though.