Welcome to HT
I'll be spending my first holiday in Malta in a few weeks (before the buses change to arriva) but I'm totally confused about how they work and how to get from A->B.

I am not surprised as it does appear a bit confusing, I will try and help out a bit.
Take a look at this route map
http://www.atp.com.mt/atp/servlet/ControllerServlet?action=listSummerBusRoutes
The most important thing to remember is that most routes start and finish in Valletta and once they reach their destination they follow roughly the same route back to Valletta mostly using the same route number. This is handy if you get lost as you can easily get back to Valletta and regain your bearings
If you click on a particular route in the link above it will give you times and any bus number changes for the return journey.
For example the 27 starts in Valletta and goes out to Marsaxlokk via Tarxien and then returns on the same route back to Valletta, looking at the map you can see that it also passes through Paola, you have a choice of change of bus in Paola, look at the map and you will see that there is a choice of buses from Paola, bus numbers 1,2,3,4,8,18,19. 27, 427 & 627.
The map also show that Marsascala (look on right hand side of map) get bus numbers 17,19 & 20
Lets look at a simple example, you want to go by bus from Marsaxlokk to Marsascala
Take one of the buses from Marsaxlokk (27,427 or 627) which passes throught Paolo, you want to get to Marsacala and you can see that bus numbers 17,19 & 20 go there, looking at the map you can see that bus 19 also goes through Paolo, so you would take the bus from Marsaxlokk in to Paolo and then change bus on to the 19 in Paolo.
Is this the route map you have downloaded?
http://www.atp.com.mt/atp/html/ATP_MAP.pdf
As I mentioned most buses start and finish in Valletta so you can also see a map of the terminus at the Triton Fountain on the above map.
There you go clear as mud
If you let me know which area you are staying I will provide an example route to a destination for you.
Grahm