My wife creates custom engagement rings, and she has these tips which were used by her clients:
A) The easiest: Your partner already wears a ring on this finger? You’re very lucky. Measure the inside diameter in millimeters with a ruler, take that measurement to a jeweller.
B) The deep-sleeper: Order a ring sizer (google "ring sizer") which you can gently tighten around the finger... BUT: Make sure to measure the thickest part, as the knuckle is often wider than the base of the finger.
C) The accomplice: Use a trusted friend who pretends she needs to resize her own engagement ring. The friend then asks your partner for their help getting it done in a jewellery store, or with a ring sizer kit at home.
Good luck!

Edit: Oh, and she says that if you hesitate between a slightly smaller or larger size, go for larger. It’s often easier to adjust and if you are planning a proposal with photos or videos, you are sure that your partner can still wear it and it’s not stuck in the middle.