Here is a Genshin Impact team guide article on how to build a Wriothesley team comp including details of the team members and free-to-play team.
In this team build, Wriothesley is a DPS that mostly relies on Normal/Charged ATK to output DMG. Since is using Catalyst as a weapon this will be easier for him to apply Cryo DMG making it easier for him to fit in any team comp.
Here is some team build that is suitable for him:
Wriothesley Best F2P Melt Team Comp
This free-to-play team is a great option for a player who doesn't want to spend Primogem or a newbie who doesn't have any 5-star characters. Even though, this is a F2P team you still can maximize his potential as well. You can use Wriothesley for Main-DPS that can output Cryo DMG to react with Xingqiu which can attach hydro element on enemies to create a freeze reaction and using Xiangling or Bennett to apply Pyro to trigger Melt reaction.
- Both of her skills can apply AoE Pyro off-field.
- Can apply hydro element to attach enemies which can react with Cryo to create a freeze and provide some DMG and protection using his EM burst.
- Can buff allies' ATK as well as heal teammates.
Wriothesley Best Permafrost Team Comp
This team comp focuses on maximizing the Freezing reaction DMG by using Wriothesley to react with Yelan, Xingqiu and Diona with healing and shield to protect the team.
- Can mark opponents that can explode and deal with Hydro DMG based on Yelan Max HP.
- Deal Cryo DMG and create a Shield that can absorb DMG and her burst can regenerate HP of characters within the AoE.
- Deal hydro on her EM Burst and apply hydro on enemies to trigger Ayaka or Shenhe to create a freeze reaction.
Wriothesley Best Melt Team Comp
This team comp focuses on maximizing DMG from Hutao pyro element to create vaporized as well as enhance output of her EM burst DMG.
- Apply CC DMG and group enemies together which makes it easier for DPS to deal more Burst DMG.
Wriothesley Best Fridge Team Comp
This team comp focuses on creating Fridge from Wriothesley's reaction to Hydro from Kokomi and Wriothesley to enhance more DMG.
- Apply AoE Dendro DMG to react with Kokomi to create Dendro Core which can trigger Fridge with Wriothesley.
- Provide healing abilities to the team as well as Hydro to react with Dendro.
End of Best Wriothesley Team Comp.