Rule variations
There are a number of variants of the Single Transferable Vote rules
DSU uses the DSU02 STV system, which is similar to the Fractional STV system mentioned below, but with capacity to deal with constraints, and more detailed rules in other places. It also explicitly includes rules for dealing with Re-Open Nominations options.
The Electoral Reform Society ruleset (ERS97) is used by most UK institutions that require an STV ruleset. It's reasonably detailed in the description, and easy to hand count quickly, but the description is a little unclear in places, and the 'last-batch transfer' policy seems to place the trade-off between count convenience and best representation too far on the convenience side for my liking.
Malta uses an STV variant for its own elections. The main variations from the ERS97 ruleset are that surpluses are transferred in the order they are received, then in size order, rather than in strict size order, that 4 decimal places rather than 2 are used, and that quota is worked out as (votes/places+1)+1. Actually, the transfer value calculation and the dealing with non-transferable difference seems a bit odd - read section 42.
This Fractional STV system seems similar to the DSU02 rules, but less detailed in the implementation. It also sets quota as 1/places instead of 1/(places+1) although I'm not sure if this can affect the results or not - I think it just slows things down. There's also an odd pseudo-STV/AV hybrid on this site that they call 'minimal STV' which avoids ballot papers having values less than 1. It also has the disadvantage that recounts may not be as practical, as the order in which the ballot papers are counted can affect the result. It's odd, but good for a really quick hand-count or a demonstration of the principle of STV.
The Australian system introduces further variations. Some parts of Australia use last-batch transfer, some transfer all surplus papers, and New South Wales does something different again. They also have a 'ticket' system where a party can set up a 'standard' preference list, and people can vote for tickets rather than explicitly expressing the same preferences.
Meek's method of STV counting dynamically adjusts the transfer values as the count progresses, attempting to use each vote optimally. It avoids the few tactical voting problems remaining with STV, but has the unfortunate disadvantage of being practically impossible to count by hand except in the simplest of cases.
Re-Open Nominations
There are two general interpretations of Re-Open Nominations or RON. After some debate, CotH now generally accepts "RON-2" as being fairer and closer to the spirit of STV.
"AV-esque" RON
When RON achieves quota, the count terminates and all remaining open places have nominations re-opened.
"RON-2"
When RON achieves quota, one place has nominations re-opened, and RON's surplus is transferred to a RON-2 option, which then may be eliminated or elected as normal, and receives any further surplus transfers that would have gone to RON. RON-3, RON-4, and so on will be created as necessary.
One place is re-opened for each time RON achieves quota.