A glass cutter. People who work with stained glass use them.

Soak string in lighter fluid tie around bottle. Burn it when firm goes out tap the bottle where the string is and it should crack away sand till smooth

I seen this clip on you tube the other day, she makes it look quite easy but i would maybe add some gloves and safety glasses first https://www.youtube.com/watch?v=8LZGzhtzcyY

Soak twine in finger nail polish remover, wrap twice around the bottle where you want it, set the twine on fire then immediately plunge into ice water. It will break neatly where the twine was tied. There is a tutorial on youtube and instructables.com.

http://www.instructables.com/id/How-to-cut-a-bottle-with-string-and-nail-polish-re/

It's pretty cool...you soak a piece of yarn in nail polish remover, tie it around the bottle, light it with a lighter and let it burn for 10-15seconds, then dip it in a bowl of cold water. Be sure to wear gloves and safety glasses just in case. It's a perfect cut every time.

A glass saw does the best job but you can buy cheap hand cutters for scoring and breaking the bottle. It's not a precise art, so have some extras (and safety goggles and gloves) on hand.

If you use the flat side of a nail, and shake the bottle up and down, lightly in a circular motion, it pops the bottom right off. Then you have to smooth down the end a little bit

If you heat the bottom of the bottle and them freeze it immediatly, it will cut that way: https://www.youtube.com/watch?v=wwwKD1VAQCo

https://www.youtube.com/watch?v=yHWYjMlYH50

You can try the string and lighter fluid method :)

I was looking at some the other day, I seen some clips on you tube using this one http://www.amazon.co.uk/Machine-Scoring-Creating-Tumblers-Planters/dp/B015CAS2N4/ref=sr_1_1?ie=UTF8&qid=1452767968&sr=8-1-spons&keywords=glass+bottle+cutter&psc=1

There's this technique where you drench yarn or any type of string in acetone/flammable liquid and you wrap it around the bottom of the bottom and set it on fire. After the alcohol burns up, you shock the glass in an ice bath. Apparently it works real nice!

http://www.wikihow.com/Cut-a-Glass-Bottle yarn method tested and approuved

Glass cutter

https://youtu.be/WxKZ8hhcmvg

https://www.youtube.com/watch?v=WxKZ8hhcmvg :)

http://www.instructables.com/id/How-to-cut-a-bottle-with-string-and-nail-polish-re/

erm....you might want to read the half a dozen comments about the same question before yours...LOL! :)