So your options are active management or physiological.
Active is recommended if you are at an increased risk of bleeding... induction, prev PPH, precipitate labour, large for dates baby, prev CS, BMI over 30, synto drip in labour, etc. There are two options for it which I decided by your midwife, syntocinon or syntometrine (syntocinon and ergoMetrine). The latter more likely to be used if your risk of bleeding is significantly higher. The ergometrine is l know to make you quite sick soon after, but obvs not in every scenario, but definitely a big side effect. A lot of units do not use this as a first line.
Physiological is an option where post birth bleeding risk is lower, so spontaneous labour, no augmentation of labour etc.
In normal circumstances baby out, given to mum, delayed cord clamping of at least a few minutes, then if you want active, have injection, clamp and cut cord, midwife applies traction to cord and hopefully delivers placenta. Increased risk of cord snapping, inverted uterus and retained placenta.
If no increased risks of bleeding and you don’t have a major preference, I usually suggest jut waiting it out a bit, no rush, sit upright (stool, chair, in pool) and see what happens.