There are a large number of yaku in Riichi Mahjong. You must have at least one yaku to be able to win, although you can have several yaku in one hand. There are three types of yaku: Closed hand only, closed or open, and "Eat and decrease", a yaku where its value decreases if the hand is open. For the sake of simplicity, these will be referred to as "closed", "both" and "value" respectively. Here is a list of some that you can refer to. Note that there are many more yaku than the ones listed, with more complex requirements.
(Closed, 1 han) Also known as Riichi. One of the most common yaku, you can declare riichi when you are one tile away from winning, also known as being in tenpai. When you declare riichi, you discard sideways, and pay 1000 points as a deposit. When in riichi, you must discard any tiles drawn that do not let you win, and you may not change your hand under any circumstance, with the exception of closed quads that do not change your hand composition. When you win with riichi, you can access uradoras, tiles underneath the dora indicators that act as additional dora indicators.
(Closed, 1 han) Also known as Tsumo. When you have a closed hand and draw a winning tile from the wall or dead wall, you can declare tsumo. All other players must pay the player who declared tsumo. If the player who declared tsumo is the dealer, the other players must pay a third of the total value each. If the player is not the dealer, the dealer must pay the full third whereas the other two players must pay roughly half of a third.
(Closed, 1 han) Also known as Pinfu, this yaku is exactly what it says on the can - in order to get it, your hand must be worth no additional points. That means no triplets or quads, no pair of dragons, no pair of your own wind, and no pair of the wind of the round. The hand must also be waiting for multiple winning tiles that can make a sequence, meaning you cannot make a pinfu with a closed, edge, or pair wait either. When the hand is won by drawing from the wall, the two fu for self-drawing is usually not awarded.
(Value, 2 closed 1 open) Also known as Ittsuu. When your hand has 3 straight melds, specifically 1-2-3, 4-5-6, and 7-8-9, of the same suit. The fourth meld and pair are not important to the straight, as long as they are still a valid meld and pair.
(Both, 2 han) Also known as Toitoi. When all four melds used in your hand are triples or quads, with no straight melds. Alternatively, if all melds are closed, your hand becomes suu ankou, worth yakuman (the point limit).
(Both, 1 han) Also known as Tan'yao and Kuitan. This yaku is achieved by having no terminals or honours in your hand. If the hand is closed, it is referred to as tan'yao. If it is open, it is referred to as kuitan. Some rules do not allow kuitan.
(Both, 1 han per honor triplet/quad) Also known as Yakuhai. Having a triple meld of honours gives your hand the yakuhai yaku. For each triple meld of a dragon, your wind or the prevailing wind, an extra han is added. If your wind is also the prevailing wind, a triple meld of said wind is worth two han, allowing for a potential 5 han from this yaku alone.