Or, How to use the tram.
This seems to be something people struggle with, so I thought I'd be brave and explain how it works, in the hopes that more people going on holiday will google holiday in Nice, and then find out all about the public transport system before they get here, rather than as they go.
(Yes, there is some self-interest here. Who'd have thought?)
OK, so, public transport in Nice itself can be boiled down to 3 main types: tram, train and bus.
The tram is the easiest, there are only two lines: one running in one direction, one running in the other. You buy your ticket before you get on the tram - each tram stop has a ticket machine, which takes credit cards and cash. You can buy either a 1 euro solo ticket (one use only, can be used for a transfer within 74 minutes onto the bus, or a later tram, but not a tram heading in the opposite direction, as far as I remember. You should check that at the Ligne d'Azur website though...) or you can buy a 4 euro day pass, valid until the end of the service for that day (or possibly midnight, whatever) rather than for 24 hours. This is valid on buses or trams, in any direction, as many times as you like for that day. You can't buy a ticket on the tram, you must buy it beforehand, and then validate it on the tram, by sticking it into the little box with a slot in. The box will whir and then spit your ticket back out. Remember to pick it up, particularly if it's a day pass.
The bus is more complicated, and I'm assuming if you're getting the bus, you already know where you're going. You can buy a ticket on the bus, the same solo/day pass options exist, and a day pass that you bought earlier for the tram works on the bus too. If you're getting a bus out of town - to Monaco, or the airport, or St Paul de Vence or wherever, the day pass probably won't work, so you'll need to buy another ticket. With the exception of the airport buses, these only cost a euro ish each way anyway, so it's not a major expense. Airport buses are more expensive - but the day pass might work with them, thinking about it. The ticket they sell you on the airport buses is a day pass - check with the driver, but don't be too surprised if you end up having to pay for a new one. Once you have your ticket, remember to validate it in the little box by the driver (don't try and get in at the back door, some drivers are bad tempered and will shout at you for it, thinking you're trying to steal a free ride) - it, too, will whir and spit your ticket back. Pick it up before walking to find a seat.
Train, well, you presumably all know how trains work. Concept is the same the world over. (If you live in the US/other transport deprived country and actually haven't taken a train before, well, let me know and I'll get more specific if need be :P ) Nice station has a lot of ticket machines all over the main concourse, and a manned counter which always has a long queue. I'd use the machines if possible - they usually take both cards and cash, even for small amounts. Once you have your ticket, you need to make sure you stamp it in the small yellow/orange composteur machines. This puts a time and date stamp on it, and without that stamp, it's the same as if you hadn't bothered buying a ticket. You're still liable for penalty fares and things, if your ticket is checked. So do remember to stamp it. They are usually placed near the ticket machines, and more sensible stations (Note: Nice isn't one of them) will have composteurs on the platforms. (In Nice, they're only at the entrance to the platforms. Compost before you run for the train.)
So, yeah, basic run down on public transport. This will hopefully stop you looking as utterly confused as the tourists who wandered through the whole tram looking for somewhere to buy their tickets...
Or, How to use the tram.