There are plenty of instructions like this around online, but they're all unnecessarily complicated and many use difficult or imperfect methods to cut the bottle. These steps are the simplest and most effective way I've found. I can cut a wine bottle in 2 minutes tops.
Step 1: Select Bottle/Remove Label
Start out with a wine bottle. They seem to be the easiest. Beer bottles are thinner, and crack more easily.
To remove the label just run under or soak in hot water. I used a metal spatula to scrape it off and a scrub brush to remove to glue.
Step 2: Bottle Cutter
or more appropriately, "score-er". I found this one online for around $15. There are many different kinds, but they all essentially do the same thing. Which is score the bottle all the way around, allowing you to use the method of your choice to turn the score into a perfect crack.
Make sure to apply steady pressure as you turn the bottle, and try not to slip. You want a straight line all the way around, and only one time around.
Step 3: From Score to Crack
This step in particular is the on in which the method is the best I've seen. It is faster, easier, and creates a much cleaner cut than most others I've seen.
Heat up some water in a kettle, but not to boiling. Pour it slowly over the crack, then pour cold tap water. Repeat until the two pieces of bottle separate. I put a washcloth in the sink so when the top falls, it doesn't break.
Step 4: Sand
Sand the top of the cut, and the edges, going from high to low grit.
That's it. Thanks for reading. If you have any questions, just ask.