Your government is probably despotism, which has a -1 output whenever a tile produces more than 2 units of food/production/trade. You should change your government to get rid of this penalty.
You have to declare war first. You start out at war with all players; at lower difficulty levels, AI players offer you a cease-fire treaty upon first contact, which if accepted has to be broken before you can attack the player's units or cities.
Because of `zones of control` game rule, the game prevents player moving freely in zones controlled (or partially controlled) by enemy forces. But you can infiltrate enemy zones by first moving in a Diplomat (or some other unit which ignores ZOC), and then moving regular units onto the square now occupied by the Diplomat. By repeating this process (and optionally leaving some units behind to keep squares occupied), you can make a path through enemy territory.
In small empires, the fifth citizen in each city is the first unhappy one. As you gain more cities, this limit actually decreases, to simulate the difficulty of imposing order upon a large empire. Thus, you may find that founding or conquering a city triggers widespread disorder across your empire. Another possible cause of mass disorder is if you lose a city with important wonders (like Michelangelo's Chapel, JS Bach's Cathedral or Cure for Cancer). Go to Tax Rates and increment luxury by 10% until you restore order in all or most of your cities. You might need luxury at 20% to 40% of your economy.
Go to the `World` / `Diplomacy Relationships`, select the nation, then choose `Cancel Treaty`. This drops you from "cease fire", "armistice", or "peace" into "war". If you've already signed a permanent "alliance" treaty with the player, you will have to cancel treaties several times to get to "war".
Go to the `World` / `Diplomacy Relationships`, select a nation, then choose `Meet`. But remember that you have to either have contact with the nation or an embassy established in one of their cities.
You can do that by placing engineer units on a transport and going to the ocean tile you want to build land on (this must be in a land corner). Tap the transport to display a list of the transported engineers and activate them. Then give them the order of transforming this tile to swamp. This will take a very long time though, so you'd better try with 6 engineers at a time. There must be 3 adjacent land tiles to the ocean tile you are transforming.
Research 'amphibious warfare', build a marine, and get them. Alternatively research 'combined arms' and either move a helicopter or airdrop a paratroopers unit there. If you can't build marines yet, but you do have engineers, and other land is close-by, you can also build a land-bridge to the island (i.e. transform the ocean).
To change the profession of a citizen: