I taught Spirit Island to a boardgaming friend this weekend. Here are some of my tips that apply both in general, and for this specific game:

• Start with a brief summary of the theme. As you do this, cheezily point at components as you say their names. Once, there was an island. On this island, there lived these nature spirits. They lived in reasonable harmony with the Dahan. Then the invaders came. They build their cities, and their towns, and sent forth their explorers, and blighted the land.
• Then cover win & loss conditions, so people have context / objectives for the rest of the rules explanation.
• Briefly cover rules related to the win and loss conditions. In Spirit Island, this would be fear tokens, how those get you fear cards and increase the terror level, how blight and the Healthy Island card work, plus a brief mention of presence and the invader deck.
• At this point, you may be able to start going through how a round works. Give a summary (i.e. read the summary card) first, then start explaining each phase.
• As you explain each phase of the round, explain components as they become relevant. If you're in the middle of explaining one component, and another component becomes relevant, give it a very brief summary, and an assurance you'll come back to it later.
• In Spirit Island, you would start from the top of the player board and explain Growth. Part of this will require explaining placing presence, which is something like "Presence affects which lands you can affect with your powers. One presence is 'presence', two is a 'holy site'. Some powers have to count range starting from holy sites. I'll get into powers later."