Several options really.
If you are in an Anarchy system then feel free to attack any ship and you won't be punished with a wanted status or a bounty.
If you are in any other type of system then you are only free to attack ships that show as wanted when you have targeted them. Attacking any other ships will result in getting a bounty and a wanted status in that system.
You will find ships at Nav beacons, USS's and Resource extraction sites or in SC you can interdict them yourself if you have that module.
If you have a kill mission for pirates then typically I find you need to find NPC ships that threaten you over the comms first.
If you have a kill warrent scanner then it is very good to increase the amount of bounty you can receive killing another ship, once scanned the extra bounty can be seen on the contact tab in your left UI.
Note even if kill warrant scanner shows a bounty you are still only free to attack ships that show as 'wanted' in your targetting UI.
Be aware that in an Anarchy system, no ships show as wanted and you will need a kill warrant scanner to pick up bounties but on the other hand you are free to attack whomever you like.
I tend to avoid attacking ships that are associated with the controlling faction for a system since it appears to drop your rep in that system. You may not care about that.
You will also find that attacking a ship makes other ships of the same faction red on your radar. This doesn't necessarily mean that they will attack you or that you are free to attack them.
As for tactics, I tend to find a suitable target, approach with full shield/sys pips, kill warrant scan, switch to a more balanced pip setting favouring weapons and then open fire from below and behind the target.
Against larger ships I also target the power plant subsytem in advance.
I also very much encourage you to equip a shield cell bank.
You can equip more than one but you would need to either assign them to different fire groups or disable/enable them as needed.
Try to keep speed at 50% for optimal turning and if you find yourself being out turned then either increase engine pips or change tactics (e.g. reverse instead).
Assasination missions tend to be elite anaconda NPCs, so probably avoid until you are at least in a well equiped viper and know what you're doing.
If your hull is breached then consider running

Keep in mind that all bounties you have collected and not yet claimed will be lost if your ship is killed.