how can one predict the position of the moon?

Answer 1

If you'd like to determine the rising and setting points for the Moon (good for 50 years either side of 2000), here's a link:
http://bodmas.org/astronomy/riset.html

If you're looking to input data into a telescope's computer, you need the ephemeris data.
http://en.wikipedia.org/wiki/Ephemeris

There are many places to find ephemerides.... here's one:
http://www.new-star.org/clear_sky_clock.htm#Lunar%20Ephemeris

You might like the US Naval Observatory's page:
http://aa.usno.navy.mil/data/

Here's some astronomical software pages....
http://www.moshier.net/
http://www.moshier.net/aadoc.html

Just for fun, here's a link for the phases of the Moon:
http://www.calculatorcat.com/moon_phases/phasenow.php

Answer 2

You could use an on line tool like the one in the source.