1. Join the Society of Friends of Bayreuth (Gesellschaft der Freunde von Bayreuth). This gets you ticket-offer priority of some kind, though the required donation to the Society is something like 200 or 225 Euros/year.
I sort of got my tickets through the Society. I joined the Wagner Society around a decade ago, with the idea that SOME DAY I would have the time and money to go to Bayreuth. The various Wagner Societies used to get significant ticket allotments, but that is no longer the case. The Wagner Society of Northern CA got two sets of tickets this year through the Gesellschaft der Freunde von Bayreuth, and I got one of them.
2. Join a Wagner Society (see the above). If you're a fan, you might want to do this whether you're trying to get Bayreuth tickets or not. Note that the Wagner Society of Northern California isn't currently listed at the link.
3. Apply directly to the Festival. Yes, you might be on the Festival's waiting list for seven years.
4. Buy from the Festival web site.
Yes, the Festival has started making some tickets available on their web site! In fact, this is how my friend Joan went: In May or June I happened to mention to her that there were tickets available that way, and ten minutes later she had Ring tickets and a hotel reservation. Her Ring seats were in the loge, the boxes at the very back of the house, not the best but she had a REAL CHAIR to sit on. A week or so later she got decent seats to Tristan.
The house is small by American standards, seating only 1900, and its layout is unusual, so there aren't what I would call bad seats. However, sitting in the front row for Flying Dutchman was really strange; the sound from the pit not as beautiful as elsewhere, but you were on top of the action AND had decent leg room.
To get seats this way, you will need to keep a eye on the web site. I do not know exactly when the Festival will offer seats there. As of now (September, 2015), they are accepting orders, via the web site and by mail, but you can't yet buy directly.
This is risky - apparently there are sometimes day-of returns, and you show up before the performance to buy. Long lines, I imagine, and nobody from the US is going to schlep to Germany in hopes of returns. But if you are living in Europe, or you have tickets to X and want to see Y....
6. Secondary market
One festival-goer- whose name and email I did not get - told me and Joan that the festival now allows some sales on a secondary market in Germany. Of course I also have forgotten the NAME of the web site where this goes on, plus it is said that if you are caught with secondary-market tickets, they'll throw you out of the house. so this should also be deemed somewhat risky.