Inside Paris (the municipality, which is basically the same thing as zone 1 on transport maps) and in the innermost suburbs, you can go everywhere with the metro (and in places RER), but buses provide a useful complement to get closer to some destinations or if the trip by metro would require a detour and changes. There's no real system. Most bus lines cross the city, but not in a straight line. For long distances (say going halfway across Paris), buses are typically much slower than taking the metro even if the metro requires a connection; unless you want to see the sights, you'd usually not stay on a bus for the most part of its route.
Lines number 1–14 are the metro, 20–99 are Paris inner city buses, and ≥100 are suburban buses. Some suburbs also have buses operated by different agencies with their own numbering system.
Within Paris, the first digit of a bus line indicates near which hub one of its endpoints is, but that won't help you much because the rest of the route could be anything (e.g. 2x buses go to or near Saint-Lazare, but if you see a 22 and want to go to Saint-Lazare, you'd need to know that the direction you want is Opera; and if you're starting from Montparnasse, the 95 will get you to Saint-Lazare quicker than the 28, but metro 13 is much faster than any bus). So knowing the first-digit rule is cute, but it won't really help you in practice.
There's a hub-and-spokes system in some suburbs, where you take a train or metro to a stop and continue by bus. The lines tend to follow commuter patterns; I can't think of a place that has a gridlike system with north/south and east/west lines. You shouldn't expect the kind of organization that's typically found in Germany in Switzerland at least, and I think in the Netherlands too: if the train is scheduled to arrive at :00, the bus is scheduled at :01, and the train is two minutes late, don't count on the bus waiting.
All the metro stations, and many but not all bus stops, have a network map. All bus stops (at least inside Paris, I'm not sure if this applies to all suburbs) except temporary ones due to construction, and all the buses, have at least a line map like this one. The line is all flattened, so this gives a poor idea of local geography, but you may recognize some familiar names here and there. I'd still recommend having a proper map with you. You should be able to get a copy of the Paris bus map with major streets in manned metro stations.
Directions like “northbound/eastbound/…” are never used in Paris, all signs list endpoints (and occasionally major intermediate stops, e.g. most suburban RER stations have clear indications of which platform to go to for Paris). So you will need to check a map if you only have a vague direction in mind rather than a precise destination.