Shikō means capturing four Bright cards without the Rain Man. It is worth 8 points.

January · Crane on Pine

March · Cherry Blossom Curtain

August · Full Moon

December · Phoenix
Any four of these: Crane and Sun (January), Curtain (March), Moon (August), Phoenix (December). The Rain Man (November willow) must not be one of them; four Brights including the Rain Man form Ame-Shikō instead.
Shikō replaces Sankō: when your three Brights become four, the yaku upgrades and you score 8 points, not 5 + 8. If you later capture the Rain Man as well, the hand becomes Gokō (10 points).
Shikō usually appears after a Sankō. When you have three Brights and the fourth (non-Rain) Bright is still unaccounted for, it's worth watching the field and your hand for its month. Capture any card of that month you can, since a matching card on the field is how you will claim it.
Track which Bright months are still live. If the Rain Man is already taken and you hold three non-Rain Brights, Shikō is the only four-Bright path left. If the Rain Man is still out, decide early whether you are aiming for clean Shikō or are willing to settle for Ame-Shikō at 7 points.
Shikō uses the same Nintendo-style Koi-Koi scoring on Hanafuda Legends whether you play ranked, casual, private rooms, or vs computer. Set yaku replace smaller versions of the same family (you do not score Sankō and Shikō together), while unrelated yaku such as ribbons, animals and chaff still add to your total when you stop.
If you are new to the combination, practise in the tutorial or against the computer first, then take it into online play. How to Play covers the turn structure, matching, and when to call Koi-Koi versus stopping for points.