Almost the only twin-hunt Doubles method that is commonly rung is Grandsire. The 2 also rings plain hunt in the plain course, but is affected by the calls. As you can see, the plain course is relatively simple - the three working bells each do 3rds, 4-5 down, 4-5 up. Note the starts - the 4th and 5th each begin by making a point to finish off their dodges. The hunt bell (shown in green) keeps hunting until a Bob or a Single is called. See here for information about Bobs and Singles.
The next method is Antelope, which has 4-5 places instead of dodges. Note that the effect of making 5ths and lying behind is that you do 3 blows in 5ths place altogether. See here for more information.
All these methods are related to the single-hunt Minimus methods. Although there are eleven plain Minimus methods, three of them have 6 blows in one place, so the doubles versions are not allowed, leaving just eight.
The other six methods are:
Breaston Bob
Spondon Bob
Reverse Grandsire
Reverse Antelope
Double Grandsire
Double Antelope
See also an article by Andrew Wood on Double Doubles methods, from the Ringing World in 1992.
You can also ring these methods with the 3 as the hunt bell, but the Central
Council doesn't recognise these as distinct methods, just as same ones starting
in a different place:
New Grandsire
New Antelope
Reverse New Grandsire
Reverse New Antelope
Another interesting group of methods has the 5 plain hunting as the other hunt
bell:
Bedfont Place
Double Portington Place
Cranbourne Place
