The MeetUp events are supposed to be the definitive indication of where each hash is. They sometimes even include directions that look sort of convincing until you try to follow them, but you may want a little more help. Let's face it, the instructions are written by people who already know how to get there and assume that you also know the area and just want a little reminder.
As for the public transport instructions, most of the hares have not used a Geneva bus for years, so it's worth looking it up for yourself before you set out. Work out a route from the CFF timetable system or the TPG timetables and maps.
Some events are quite easy to get to on a bicycle. The Ville de Genève has a detailed cycle map.
The instructions in the hash flashes sometimes turn out to make little sense on their own, or be impossible to get back onto if you make a wrong turn. If you're staying in Geneva for any length of time, use google maps or get yourself a copy of the Maxi Plan Sur Le Grand Genève (yellow cover) - an extremely good map of the canton of Geneva, including bus stop information (and the bus routes themselves, though it's likely that some of these will have changed since the map was made). It's also very good for working out where to set a trail (hint hint - contact your friendly local trailmaster now!). If you're staying less long, at least try to pick up a Unireso (local public transport) plan de réseau, free from one of the TPG agencies (in the main train station (Gare Cornavin)). These should be a great deal more useful than the dodgy standard tourist maps in making sense of the instructions, whether you're using public transport or driving. Failing that, try putting the location into one of the following: swisstopo or search.ch
Geneva offers a good public transport service to most of the canton and to some places in Vaud and neighbouring France which get used for hashes. There is a combined fare system (Unireso) which allows you to use a single ticket which is valid on trains, trams, buses, trolley-buses and mouettes within the region. Tickets (other than the "Saut de puce") are valid for a specified period of time from purchase (or occasionally validation, for some buses from France) within a certain number of zones.
Gare Cornavin is the main railway station, on the northern bank of the Rhone. Its bus/tram interchange includes stops on three sides of the station, together with two other stops close by (22 Cantons and Chantepoulet) so you'll need to be sure you know where your particular bus leaves from.
Place des Nations is the square outside the UN building near the large "wooden chair", which may be a useful starting point for many visitors on business.
Rive, Bel-Air and Stand are along the southern bank of the Rhone, where most of the shops are.
For most journeys you need to buy your tickets using a mobile app, online from Swiss Rail or TPG , or at the TPG/Unireso/CFF machines located at most bus stops and railway stations. The mobile phone apps are most useful: TPG Mobile App or the SBB Mobile App. The ticket machines don't give change, but do take payment credit/debit cards.
Bus costs can be found here. You'll need to do careful calculations of how many zones you're going through if you're going to any of the areas marked in blue (Vaud and neighbouring France).
Day tickets can also be purchased; longer duration passes are available from the Swiss Rail or TPG Bus agencies.
The tickets from the machines at most bus-stops are also valid on the local trains as long as they cover enough zones and time for your journey.
If you travel beyond Celigny (for example to Nyon) you'll need a normal train ticket.