Winston and Julia have noticed each other for a long time. He watches her and secretly hates her and all she stands for as a loyal Party member during the Two Minutes' Hate. She watches him and tags him as someone who is not loyal. Both admit to the other later what he/she thought of each other, which should have made them more careful.
Their first actual encounter came after the Two Minutes' Hate when Julia "runs" into Winston and falls down. When he helps her up during the seemingly innocent connection, he realizes she has slipped a note into his hand. When he is able to open it in private, he reads, "I love you".
Later, they plan to meet in a secret place--the wooded area in the park--away from microphones and cameras where they are intimate for the first time. They continue planning clandestine meetings until they are able to secure an apartment where they escape the Party (or so it seems) to enjoy each other and life as the Proles do.
Winston and Julia meet at the Ministry of Truth or Minitrue, where they both work. They keep eyeing each other obliquely. Winston doesn't know her name, but calls her the "dark-haired girl." He thinks she is spying on him, because he has noticed her glancing at him. He especially believes this after he sees her on the street near Mr. Charrington's shop.
They make contact when, outside a lavatory at work, Julia pretends to fall down. Winston helps her up and she slips a note saying "I love you" into his hand, all right in front of a viewscreen.
They meet in a wooded area outside the city. It is not until this point that Winston learns her name is Julia. He tells her his prior feelings:
'I hated the sight of you,' he said. 'I wanted to rape you and then murder you afterwards. Two weeks ago I thought seriously of smashing your head in with a cobblestone. If you really want to know, I imagined that you had something to do with the Thought Police.'
Julia is delighted that her "front" of a good Party member is working so well (she thinks), but the passage is important. At this point, Winston is still more or less dehumanized and sexually frustrated, filled with fearful and aggressive feelings--in other words, just the way the Party wants him to be. Now that he has met up with Julia, that will change.
Julia and Winston meet at the Ministry of Truth where they both work. Winston recognizes Julia as the dark haired girl whom he thinks is spying on him and works in the Fiction department. They keep seeing each other and occasionally exchange glances but never speak until one day when they meet along the corridor and the dark haired girl stumbled and fell. Winston helped her up and they parted ways after she slipped him a note reading “I love you” in his hand. They manage to whisper to each other at the canteen during lunch and agree to meet at Victory Square where they arrange their first meeting away from the crowd in the woods. It was during this meeting that the dark haired girl formally introduced herself as Julia. She already knew Winston’s name. After this, they continued to meet in different places but for less than thirty minutes each time, they took precaution. Eventually, they used the room on top of Mr. Charrington’s junk shop until their arrest.