You can get trophies by fighting PvP only ( person vs Person ). You're getting trophies in cases:
1. Your fleet attacks a city of a player and your level is lower or not more than for 5 levels higher, than his. In case your level = 5 or lower you can attack any player's city and get trophies.
2. Your fleet attacks other players fleet. In this case the amount of trophies you can get depends on the ships in both fleets. If less powerfull fleet attacks more powerfull fleet and wins the winner gets more trophies. In this case power of a fleet calculates only depending on ship types. Weapons and ship levels don't affect. (see the table below). For example a fleet containing 1 Howker with no weapons will be more powerfull than a fleet containing one shallop fully loaded with weapons. The shallop will win and the owner of the shallop will get around 40 trophies (a lot). In case of almost equal fleets, winner gets ~20 trophies.
3. Score shift. In case your score (trophies) is much lower than the score of the player you have defeated, you get some additional trophies, even if your level is higher than his more than by 5 levels. You can get 1 additional trophy for each 10 trophies of difference, but not more than 20. For example, if you are level 10 but your score is 182 and you attack and win a level 3 player with score 182, you get nothing, but if the player has 400 score you'll get (400 - 182) / 10 = 21.8 But not more than 20, means you'll get 20 trophies. This rule works backward too. If a player with 400 score attacks a player with 182 score, he will get 20 trophies less.
4. Winner shift. Winner gets additional 5 trophies to the result score for the victory.
5. Any time someone wins and gets trophies, the loser lose the same amount of trophies If someone attacks your island or fleet and lost, you get trophies, if wins - you lose trophies.
Winner cannot lose score In case when a strong player wins against a weak player, winner doesn't lose score. The minimum amount of score winner can get is 0.
Island attacks bring you trophies ( if the player you are attacking has more trophies than yourself ) and obviously you can take there resources, the island holds. Obviously there is a limited amount you can take from a player, a certain percentage usually a 3rd of what the person actually has! or if this person has millions you will take away what your ships can carry! Now don't rush into attacking island because it can go wrong!!!!!! if you lose.... you lose trophies , and weapons!!!!!! and for your troubles get a huge repair bill.
So what advice can i give you... well
Personally i like to spy on my oposition , have a look around the island see if you can guess there town hall , by what buildings they have , how many small / medium / big house do they have , can you guess there population and fleet ? what type of boats do they have , how many crew can fit in them boats ? how many foundries do they have.... think are they hiding ships in a mystical chest and secretly ready to defend against you with canons in there storage ( wink wink nudge nudge ) . are you being trapped only time will tell
Always look for pier space... that is my last clue!
look at the picture above ^25 trophies won^ from island attack , who had 200 more trophies than me... i got resources and trophies for my spolis, but will you be so lucky!