Wind, wind, wind the thread around the bottle, taking care to push it close together. To be fancy, we used 3 shades of green floss with white. It was a little tricky to get things going at the start...but once I spread a ring of craft glue (using a Q-tip) around the bottom edge of the bottle to hold the first few layers of thread in place, we were in business. Also, I spread a little glue on one side of the bottle (just a half inch line at a time) so each time the thread wrapped around, it was glued. The ends were secured with glue when we changed colors. It was a little hard to keep the thread tight together around the curved neck--needed to use a lot more glue and work slowly. We decided not to attempt our other very curvy bottle.
I recommend this project for ages 6+. It was a little difficult for my 3-year old and required my constant help. It does take some time...our bottle was 12 inches tall and took all 7 skeins of floss. Yarn would probably make the job go a little faster and result in a great-looking vase too.
We have big plans to make some flowers for our colorful new vase...another day. For now we'll let just let it revel in it's green, textured (and slightly gluey) new glamour.