The first method is Cambridge, to which many of the others are related. The basic rule here is "Dodge two, Make places, Dodge two, Miss two." e.g. Dodge 7-8 up, Dodge 7-8 down (and become 8ths place bell), 5-6 Places down, Dodge 3-4 down, Dodge 1-2 down, Hunt through, missing 1-2 up and 3-4 up, then Dodge 5-6 up (5ths place bell).
Yorkshire, Lincolnshire and Rutland all use the same work above the treble, although in Rutland 7ths is not made under the treble at the half-lead, so you don't get the whole of the Cambridge backwork. Pudsey is also Cambridge below the treble, but above the treble, the single- and double-dodges in 7-8 come round the other way, with additional places in 5-6 and triple-dodging in 3-4 across the lead-end.
Superlative is similar to Cambridge in some ways, but is a double method (so in theory you only have to learn a quarter of it, then rotate this blue line, as well as reflecting it). The Cambridge places have an extra place and dodge on one end, so that you go back the way you came, while there is a 5-pull dodge in 1-2 and in 7-8. Just beware that 5ths place bell starts by making 6ths, unlike Cambridge.
Yorkshire, Lincolnshire, Pudsey and Superlative all have the same 2673485 lead-end order as Cambridge.
Bristol is another double method, but is the first of the Standard 8 to include wrong places (although the start of the lead is right-place, which always fools me in spliced!). It is also the only 8ths place method of the group, so don't be tempted to make 2nds over the treble. Bristol is well-known as a very musical method, with "mx" lead end order, which means that you get the "repeating lead" property at bobs.
London also contains a lot of wrong hunting. It has the same work of London Minor in some ways, but in a different order. However, the basic rules of construction are the same (and also work on higher numbers): wrong hunting on the front, apart from the Stedman work at the start of the lead, so you make a place after passing the treble coming in. Also wrong hunting while the treble is in 1-2, fishtails above the treble when the treble is in 3-4, then treble-bob when the treble is in 5-6 or above. Here are some notes on the method.
The Nottingham 8 was put together as an alternative to the Standard 8, to include a greater variety of methods, as so many of the Standard 8 are Cambridge-related. So here there is a variety of work both above and below the treble, with some different lead-end orders too.
Cambridge, Superlative, London and Bristol remain, but they are joined by:
Lessness, Cornwall, Cassiobury and Glasgow.