Learning to play
These notes apply whether you want to learn to play the bouzouki, the tzura, or the baglama. They even apply to tetrachordo instruments as well as to the trichordo. Sadly, as I play horribly badly, I can not teach you how to play, so there are no actual lessons here. These are the methods...
Being born gifted
More than one person who used to post anonymously on the long vanished Skeezo forum claimed to have used this method. Apparently, these people were born able to hear any tune and immediately play it much better on the bouzouki, where better means faster, louder and with more ornamentation. They also frequently claimed that only a Greek can play these instruments properly, only a Greek can sing the Rebetiko songs, people who are not Greek can not enjoy the music as much as Greeks do, and so on.
Presumably these bigots also believe Eric Clapton can't play the Blues.
Of course, there are also some very nice people who actually are virtuosi, but most of them just get on and play, rather than hanging around on forums, gratuitously insulting people.
Learning by playing
This is the method adopted by Markos Vamvakaris, and many others. In his autobiography (available in Greek, and now also in an excellent English translation by Noonie Minogue) he says "Shortly before I was called up, in 1924 or early 1925, I happened to hear Nikos playing bouzouki and I liked it so much that I swore an oath that if I didn't learn to play I'd cut my hand off with the meat cleaver... he couldn't believe it... in six months I'd become a `terror' on the instrument.... No one had given me lessons. My only school was the teke."
You can probably do this without visiting the teke and consuming lots of hashish like Markos did (it's up to you), and it may take more or less than six months. Listen to a lot of Rebetiko, and then take hold of the bouzouki and try to do the same as the people you hear. If it takes you less than six months, you were probably a member of the "born gifted" group and hadn't realised it.
If you are learning to play the guitar, there are massive amounts of tablature on the internet, and most of it is correct. I used to search for bouzouki tablature, but the links never lead to much that is useful. Your best bet, unless things have improved a lot, is the next one.
Having lessons from a player
This is the method most recommended by people who do play. Not all music teachers are the same, so personal recommendations are useful if you can get them. Finding a teacher can be difficult, a lot depends on where you live. There are various web sites where you may be able to find a teacher. Google can be valuable here.
When using Google to find a bouzouki teacher, it helps if you include "-irish" in your search, as there are thousands of people out there who can teach you to play the Irish version of the bouzouki. As far as I know, most of them don't teach Rebetiko.
Lessons on DVD or video
There is a course on three DVDs from BouzoukiDVD that currently (2008) sells for US$225. The sample material that I saw was excellent, and the comments that I have read made by people who are using the DVDs have all been positive.
A little bit of Google searching found me another page with a video course, in Greek, with a long downloadable sample lesson. Better lighting would have helped, but this site looked helpful. I was a little worried by "Failure is not an option in his classroom" in the section about the teacher... The site has now vanished, but others will appear, no doubt, so keep Googling!
There's a lot of helpful stuff, and some quite unhelpful nonsense, on YouTube.
Learning from books
This is probably easier if you already play some other instrument, especially if you can read music notation. There are some excellent books on the subject, as well as some really bad ones. I have a separate page about the books I have seen.
Other hints and tips
Using a metronome
If you are teaching yourself, I am told that playing the dromoi in time with a metronome is a very good way to build in the knowledge your fingers need. Dimitris Mamalis - thanks for that tip! You don't need an actual metronome if you have a computer, there used to be a splendid program by David Johnston, called Weird Metronome available free, that could be programmed to play absolutely any rhythm you can think of. It has to be the most amazing 24K of code I have ever used. If you can find a copy, use this to get yourself into the Zeibekiko way of playing...
Exercises
There used to be videos of some good picking exercises on the sadly demised Skeezo web site. Basically these are patterns for your left hand to follow on the fretboard, while you play the string with your right. The idea with any exercise of this kind is to get your left hand to be able to do pretty much any sequence of notes that might be needed, and at the same time train your right hand to pick the right string without your eyes actually needing to look at the bouzouki at all. I will be very surprised if there's nothing similar on YouTube.
Chords and rhythms
Of course, you will also need to practice playing chords, and playing in the many and varied rhythms that this wonderful music uses. I hope to find some useful links soon for these... this site is always "under construction".
Downloading from the Matrix
Wouldn't that be nice?