Start by removing the shower curtain from its rod before cleaning to ensure that accumulated dirt, hardened grime, or remnants of old lubricant are completely wiped off.
Moderation is key, as applying an excess of Vaseline could lead to it dripping down or possibly staining your curtain. Once applied, rehang the shower curtain.
The curtain should now glide smoothly across the rod, free from resistance. Repeat the process every few months or if you notice the curtain starting to stick again.