How Much XP Do I Have
Firstly to see how much XP you have and how much to the next level, hover your mouse over the transparent and green filled curved slot below your Portrait (top left). A pop-up will display your experience level in detail for you.
Clear your Home Island
At first, you can only gain XP through completing quests found in your quest book. Later, you will use military units to clear bandit camps for adjacent sectors. Each bandit camp awards you with a certain amount of XP, depending on the units in the camp.
When a season event is in progress, if you are a high enough level to take part, you will probably get Adventures that are pretty easy to complete and give huge amounts of XP compared to regular Adventures for fairly small losses.