what do I need to make 230V AC fan spin slower?
Yes, you want a series capacitor. For 230v mains, it should be 400V rated (because of the peak being 1.4-ish times the RMS). If it's a typical 80- or 120-mm fan as used in computers etc, you'll probably want a cap of around 220nF to 2uF, depending on the fan and how much you want it to slow down. For a bigger fan you'd need more microfarads.