Hi. Just to give you more resources, here's a link to the wiki's Main Page.
To try to answer your questions:
To find places with PVP enabled, look at the Galaxy Map, specifically the Darkness Map.
This is the map of the systems owned by the administrative teams, or "Darkness." Red dots are where PVP is enabled. If you click on the red dot, it will take you to that System's webpage. Each system page will tell you whether PVP is enabled on ground or space.
For an explanation of each type/part of combat, you could start with this wiki page: Combat Wiki Page
. It links to other pages that describe things more clearly. It's a little outdated but it should give you enough info for now.
You can also check out the rules pages for ground combat
and space combat.
They should be accurate enough for your needs.
If you want to learn more about combat, I'd recommend creating a character and starting the tutorial.
As to how various factions fight, that's a longer discussion. I've only been here for < 1 year, so I'm not an expert.
For actual combat right now: Different groups can meet up in a combat-enabled system/planet and fight. Or they can agree to fight in the space combat simulator, called "Warsim" or "Showdowns," which follows the same rules. They might agree to external consequences based on the outcome of such matches (such as exchange of territory). Many factions are preparing their offenses/defenses for when PVP expands further.
Factions also regularly fight bandits in Asteroid fields and bandits & creatures on uninhabited areas of planets (as Evan mentioned).
Beyond combat, there are a lot of other ways that factions compete for power. Factions frequently compete for new territory, compete economically, and to some degree compete for members. There are also (but less frequently) political upsets (like treaty changes), information trading, spying/sabotage, government collapses, double agents, and assassination attempts (depending on what combat is available at the time/place).
Hope any of that helps!