Early game with this build is essentially the same as any normal early game Seraphine. Use Q to clear out waves and to poke enemy champions.

During the Mid game, forcing teamfights is a good way to get ahead as it is very easy to get kills and assists with Seraphine's kit.

Always stay with your team in the late game. If you absolutely must split push then bring a teammate along as your low mobility makes it very difficult to escape if the enemy team decides to put a stop to your shenanigans, even with your high amount of cc.

Your Passive will increase your auto attack range, each note provides a small boost to attack range. It will also cast every 3rd ability twice.
Your Q does more damage the lower health an enemy is.
Your W will heal you and nearby allies if you have a shield when casting. This is why mountain soul is essentially a win condition on Seraphine and why playing with champions that can provide shields is so effective.
Your E will slow enemies. If an enemy is already slowed, they will be rooted instead. If they are already immobilised, they will be stunned instead.
Your R's range will reset when it hits a player (both allies and enemies). This basically acts as if you cast the ability at the location of the player that was hit. This effect will chain.

Early game combo: E -> Q
E will slow/root enemies making it easier for you to follow up with Q for damage.

Fight Starter combo (after getting everfrost): R -> Everfrost Active -> E -> Empowered Q
Using R will allow you to easily line up an everfrost charge, which when followed up with an E will stun the enemy team giving your team a short window to deal lots of damage to as well as get your own damage off with Q.

Buying Everfrost before Rylai's is best as it provides more benefits overall. The extra mana and ability haste help you throw out more abilities, especially more E's and R's. Rylai's passive ability applies a slow to any enemy hit with an ability. This slow is applied BEFORE your E's slow, thereby converting it into a root when unempowered or stun when empowered. Cosmic drive and Lucidity boots used to increase ability haste and help you pump out more E's and R's and prevent the enemy team from moving at all.
Morellonomicon is useful against heal/lifesteal heavy champions/teams (e.g. Samira, Yone). Banshee's Veil is useful against cc heavy champions/team comps (e.g. Veigar, Malzahar). Demonic embrace is useful against tanky champions/teams (e.g. Rell, Malphite). Deathcap is an item I'd only recommend if you are far ahead and your team has much more physical damage than magic damage.

If the enemy team relies heavily on their high mobility to perform properly (e.g. champions like Volibear, Singed, Janna, Pyke, etc.) or is very weak to high amounts of crowd control (e.g. champions like Rell, Yuumi, Jinx, etc.), then this build is perfect to use. The insane cc provided by Beat Drop (E) when combined with Everfrost's active ability and Rylai's Crystal Scepter's passive abilities is sure to make your enemies tilt, which means it is also a great build to use if you enjoy trolling your enemies and/or making their lives living hell. Your enemies will be forced to buy Quicksilver Sash, which in many cases messes up builds and can only protect against so many combos.