Bounties are issued for crimes, different crimes will bring different amount of bounties issued with murder being highest. If you have any fines and do not pay those they will turn into bounties after some period of time (currently 24 hours but it will be extended in 1.3). Highest fines probably can be received for smuggling big amount of illegal goods. For now there is a limit of 1 million per minor faction of how big bounty one can have, but in 1.3 there will be interstellar bounties for serious criminals.
With basic scan - targeting a ship and performing a scan - you can see only bounty under current jurisdiction. In anarchy systems there are no laws thus no bounties and to see if ship is wanted anywhere else you will need to buy Kill warrant Scanner module. You can buy it at almost any station which has Outfitting section - it's under hardpoints->Utilities. There are many variants of KWS that differs by power consumption, range of scan and price. The scan speed is always the same and is around 10 seconds - you must assign KWS module to a fire group, select target and scan it by pressing fire button, just keep in mind that you must keep it pressed for the whole scan time and target must be within huge brackets on your front view - if it moves outside the scan will break and slowly deteriorate, but if you keep fire button pressed and return target within those brackets the scan will keep going on. It takes some practice but it's very easy.
So if you want to maximize profit from bounty hunting you should buy Kill Warrant Scanner as it allows you to see bounties not only from current jurisdiction but all issued bounties on that ship and upon that ships destruction you will receive bounty vouchers for all crimes and not only from current jurisdiction crimes. If NPCs release chaff that might mess up with your scan but not for long.
More about Kill Wartant Scanner.
This is probably my favorite spot for hunting pirates - great view, nice enemies and if you are in a right instance you can get loads of wanted anacondas, dropships, clippers and pythons in very short amount of time.
To reset NPC ships in an instance you need to save to main menu and load the game or enter super-cruise and exit back, if there are no other players then instance will be reset and NPC ships will change, that way you can find more interesting targets faster because NPCs spawn slowly.
But if you get into right instance you should see mostly right ships for quite some time, once i earned 2 million credits in around 20 minutes, so if you see there wanted large ships keep killing them but if all you see are wanted sidies, adders or cobras just reset the instance.
In next build, 1.3, there will be high and low intensity extraction sites - at high intensity you will encounter much more pirates and mining metals will be better, but at low intensity sites you will have greater police presence and less of a chance to mine expensive metals.
More about mining.
Those can be found near stars in almost all habitable systems. Just select Nav Beacon from Left User Interface->Navigation tab and exit like with any other navigation target when you see Safe Disengage sign appear.
There you can find all kinds of ships - from sidewinders to anacondas. if it's not an Anarchy system there will be police ships as well, so you can go there and play safely even in small/medium ships. Make sure you perform basic scan before attack because if you don't there will be issued bounty on you even if the enemy ship will be revealed as wanted afterwards. In anarchy systems all ships are "clean" so you need Kill Warrant Scanner.
To reset NPC ships in an instance you need to save to main menu and load the game or enter super-cruise and exit back, if there are no other players then instance will be reset and NPC ships will change, that way you can find more interesting targets faster because NPCs spawn slowly.
Keep an eye on how many ships per wing are there before attacking, so you will not be surprised that after your first shot you have 4-5 red blinking white enemies on your radar.
More about User Interface.
At most signal sources you can encounter wanted ships (in Anarchy systems you need to have Kill Warrant Scanner to see if any ship is wanted elsewhere).
Weak Signal Sources: mostly only containers.
Unidentified Signal Sources: small and medium wanted ships, sometimes with police presence sometimes no wanted ships. I saw several times there wanted anaconda fighting police vessels, but mostly just sidewinders, eagles, vipers, cobras.
Strong Signal Sources:
Most challenging signal sources, wing of anaconda and support ship, 3-4 wanted anaconda wing, 5-8 vulture wing, 3-5 vulture wing against several fer-de-lances etc. There will be greater diversity in future but do not go to strong signal sources alone in small/medium ship unless you know what you are doing. If you see 4-8 containers of gold then it's famous gold trap - expect some trouble in a form of 5-8 vulture or 3-4 anaconda wing.
You can basic scan any ship and if it's wanted (in non Anarchy systems only) you can interdict it (need Frame Shift Drive Interdictor module installed in any of your ships internal compartments). Interdiction in some systems is considered as a crime and you can get fine issued for that. Also keep in mind that you cannot use Kill Warrant Scanner in super-cruise thus you can't check if target is wanted in any but current jurisdiction.
More about interdictions and Super-Cruise.
Players tend to stick around well known trade routes (like Gliese 868), rare good routes (like Lave) and community goal systems.
More about community goals.
Any ship is good for PvE but best are with high firepower and well protected ships, so best ship for PvE is fully kitted Anaconda - it has huge firepower and insane protection, second would be Python because it is like small Anaconda, then comes Fer-De-Lance, Vulture, Clipper or whatever you like, but i would say that Anaconda and Python are best because they can kill fast and have strong enough shields to withstand most if not all attacks. Anaconda is only ship that cn not only easily survive 8 wanted Vulture wing attack at Strong Signal Source but kill 'em all!
As for weapons then for PvE i would recommend beam laser and multi-cannon/cannon combo, but anything works fine as long as you destroy enemy power plant and not try to blow up large ships by destroying their hull. Large pulse lasers also do the job great and they are not that demanding on power (so more power for shield boosters and shield cell banks) and not that demanding on Weapon capacitor so you can shoot long enough. On small/medium hardpoints beam and multi-cannon is used mostly while on large/huge hardpoints pulse laser, beam laser, cannon, plasma accelerator is used effectively against NPCs.
More about Outfitting, Weapons, Bulkheads, Shields.
PvP is completely different beast as you need to lower enemy shields as fast as possible and make them run or at least have a chance to blow their thrusters, frameshift drive or power plant (if you are in a for a kill). It also depends a lot on if you are fighting 1 vs 1 or wing vs 1 or wing vs wing, so there is no easy simple answer.
Many pirates prefer Clippers and it's one of the fastest ship in the game now so going after it will require wing of clippers, while vultures can be killed in clipper, ferdelance.
Python and Anaconda is just too slow to kill anything faster unless enemy has a death wish, so those ships are only good as a support, however, if there are wing vs wing then support ships might turn tide of war to your favor.
Anyway i would name for PvP such ships: Fer-De-Lance, Clipper, Python, Vulture, Anaconda, occasionally i see Asps or even Cobras but mostly now are flying bigger ships.
As for weapons then it all depends on your ship, flight skill and enemy ships.
Large Beam laser, medium Rail Gun, large/huge Plasma Accelerator to get rid of shields would be my top choices, large/huge Cannon, medium Rail Gun, large Fragment Cannon, medium multi-cannons would be choices to finish enemy power plants, but it really depends on ship you are flying - if you can get very close and personal then plasma, cannons are great, if you prefer some distance between you and enemy then Rail Guns, Beam lasers are a great choice.