Furina’s gameplay is fairly simple, mostly ensuring that she maintains uptime on her Skill while ensuring her Burst’s buff is stacked up as much as possible before major DPS windows. Paired with her fairly long duration on both abilities, this means that Furina typically uses her abilities at the start of the rotation, though she can also opt to split up her Skill and Burst cast to ensure Burst uptime when it matters most. Note that her Skill’s ending animation can be Dash cancelled, and doing so will likely make her feel smoother to use.
While most healers can sustain sufficiently against Furina’s HP drain, her Burst benefits significantly from characters with a large burst of team-wide healing such as Jean and Escoffier. They allow Furina to instantly accumulate a lot of Fanfare to maximize the strength of her buff, though it isn’t worth forcing them onto the team if not already synergistic. If Furina would fit well on a team but the team lacks a healer, it’s worth considering if any of her party members can use Prototype Amber without a significant loss. Note that it tends to break even with Furina’s drain, so it cannot be relied upon for sustain.