There are so many ways to combo. Seriously, it's rare that you'll combo the same way in multiple games. It's all about knowing how and when you can go for it. I'm gonna list some of the key cards below, and then highlight some example combos.
Amulet of Vigor: Easily the most important card aside from Patron himself. This card allows for so many of the combos because it makes it so all lands that you put in with the Patron's ability come in untapped, which I will highlight the Importance of later. You'll want to find this card almost every game and be able to protect it.
Storm Cauldron: My favorite card in the deck. I've always loved this card, and honestly I don't know why. It screws your opponents over while simultaneously accelerating yourself and allowing for our first combo: Amulet of Vigor + Patron of the Moon + Storm Cauldron
. Tap 2 lands, they both return, pay 1 to put them both back in untapped. It's infinite mana and infinite landfall triggers, which can both win the game.
Altar of the Brood: One of the wincons. Couple this with the combo above and you can mill everyone to death. There are more wincons other than this, but this is the one I find myself utilizing most of the time because of how easy it is to find.
Meloku the Clouded Mirror: Great card. Can be used for value, or it can be used to combo. Replace this guy with Storm Cauldron in the above combo and you get infinite flying creatures, but lose infinite mana unless you have a mana doubler. He's also a moonfolk, so that's a flavor win. You probably won't be saccing him to moonfolk offering though, he's too good.
Nykthos, Shrine to Nyx: Almost a no-brainer. It's great at accelerating, and like Meloku, it can also be used to combo. For example, it can be used in the above combo with Meloku, and with 1 additional blue symbol and mana, you can also produce infinite mana. There's a lot more than this but I'm gonna refrain from mentioning cards I havent talked about yet, like the next one
Oboro Breezecaller: Another Moonfolk that combos, hooray! This card can enable one of the few combos that doesn't require Amulet of Vigor. Nykthos, Shrine to Nyx + Oboro Breezecaller + Patron of the Moon
. Assuming you have enough devotion, make mana off Nykthos, untap it with the Breezecaller, repeat, use Patron to put the lands you bounce back in, and it obviously doesn't matter that they're tapped.
Retreat to Coralhelm: Really good value card, but more importantly it provides infinite scry in basically every combo. This can allow you to get whichever wincon you need at the time. If the coast is clear, I usually go for Altar. If it's not, get Sphinx of the Final Word and then Blue Sun's Zenith to make your opponent draw their deck. It also allows for one of the most convoluted combo I've made with the deck, Meloku the Clouded Mirror + Retreat to Coralhelm + Walking Atlas
Trade Routes: Cool land bouncer. You need plenty of these effects. With amulet this can be infinite landfall, with Retreat it's infinite scry, with a mana doubler it's infinite mana. If you get infinite mana, you can then return all your lands and draw off of them, which will usually allow you to get something that wins.
Sunder: This doesn't make an infinite combo, but damn if it doesn't put the game away. Cast sunder floating all your remaining mana, use Patron to put all of yours back in. This is easier with Amulet, but it's not always necessary. Pair it with Sphinx of the Final Word to make sure it gets through. If I end up with Merchant Scroll in my hand this is typically what I get.
Training Grounds: This card isn't always good, but when it's good it's excellent. It turns Sphinx of Magosi into a monster, Memnarch costs 3 less to steal stuff, and it turns the moonfolk into really efficient creatures and even combo pieces. The most crazy combo I've actuallly done in a game is Patron of the Moon + Amulet of Vigor + Training Grounds + Soratami Mirror-mage. Pay 2 to bounce 6 lands while leaving the trigger to bounce a creature on the stack. Pay 3 with the patron to put them all back in untapped, repeat, netting 1 mana every time. If you're playing online this takes absolutely forever to do, hopefully your opponent will be a good sport and concede LOL