Farming is a big part of the game right now. It takes a ton of food for guilds to keep their territories up. This is why farming and breeding are currently realy profitable. The only way to get a personal farm is to buy a personal island. You can do this at any city with a harbor

Cities where you can buy an island:

 Buccaneers Haven

Smugglers Bay

Fisher's Hold

Journey's End

Breakwater

Seamouth

Freeport

The setup i'm using requires 2 farms and 1 pasture. I'm doing this because it requires quite some food to breed your animals. You can build a farm or a pasture by pressing the "b" button on your keyboard and go to the farming tab. Once you have placed your farm or pasture you have to gather the required resources to build them. A farm requires 15 T1 Stone and 15 T1 Wood. A pasture requires 25 T1 Wood, 25 T1 stone, 25 T2 refined wood, 25 T2 refined stone. This gets us to a total of 40 T1 wood, 40T1 Stone, 25 T2 Wood, 25 T2 Stone.

Once you have built the farms and pasture you have to get some seeds to make carrots. You can go out and kill some mobs to try and find seeds but the fastest way is to buy them at the Auction House. A farm can have a maximum of 9 seeds. If you have the silver to buy 18 seeds go ahead and buy them.

After buying the seeds it's time to head back to your farm. You can plant the seeds by clicking them in your inventory and pressing the "Place" button.

After planting the seeds all you have to do is wait for the time to pass, go ahead and gather some resources or slay some mobs while you wait.

Once the carrots have grown, you can harvest them by clicking on them. When harvesting them you will get some fame and after 18 patches you should be able to breed chickens.