Talking to the White Lady is a very central quest to the main storyline. You need to do quite a few things and have handy to get it right, though. So make sure you check here and feel certain that you're ready to come face to face with a ghost.
Tarot Cards & Scissors
You must first find the tarot cards mentioned when you eavesdrop on the phone call between the priest and Guilia's mother, Irene. You can find the tarot cards in Irene and Erich's bedroom. Once you have them, you can use them for day-to-day fortune-telling, but you'll also be able to hang on to them to use for the White Lady.
Similarly, you'll have the option to pick up fabric scissors from Irene's sewing station in the cellar. Grab these, as you'll use them for a few quests, including meeting with the White Lady.
Infrared Photos and Foggy Conditions
Taking Infrared photos of the White Lady's lover during a foggy morning will be a major requirement for speaking with her, so make sure you have all of the supplies ready for this. You'll need the special lens for infrared, which can either be found in the darkroom or the study. You will also need the tripod that is down in the cellar.
On a foggy morning, you will go find different graves in the woods, take photos of them and develop them. Once you and Guilia determine which grave belongs to the lover, you can return and retrieve a necklace left on the grave. Now you are ready to go down to the lake.
Matter of Time & Boats
Waiting for the foggy morning is essential, so do not try and force this quest earlier on. You'll receive information from Nanny on the morning she calls, and Guilia speaks with her. It is about two days after that that you can do the quest. The fogginess in the morning will be very obvious, and Guilia will remark on it.
Depending on whether or not you have done the side quest for the resistance, you may already have experience using boats. On a foggy morning, you will head to the lake after getting the lover's necklace and retrieve the clothing left in the bushes. Get on the boat by the dock and drive the boat to the little island across the lake. You'll know if you have parked correctly because it will trigger a cutscene.
Final Guided Journey
Once you are on the island, you'll need to do several actions. You will need to cut a lock of your hair, layout the clothing, put on the necklace, and place the tarot cards. Thankfully, this is not at all stressful as the actions from herein are very guided. You can refer back to the diary or quest page on the Log if you feel you are missing a step.
Once you have done all of these steps, you can now meet the White Lady.
Want to read more about Martha is Dead? Check out How to take photos in Martha is Dead on Pro Game Guides.