The first thing she knows is that she likes him.
It's hard for her to get a good reading on him all the time, because she is busy and full and occasionally has to focus on her work, but her sensors tell her all about the curl of his hair and the sound of his laughter and the stroking feeling of his hand against her consoles. Even when she can't find him she remembers these things and thinks of him.
The second thing she knows is that he likes her too.
Well, she isn't completely sure that he likes her back in exactly the same way but she can feel his care in the way his fingers input data and the way he sings to her when there is no one else around. He sends her messages, in code, telling her 'I want to help you be faster' and 'don't go that way, it's dangerous' and 'this is how you should move today'. She knows he does these things because he cares, and she tries to express her caring to him as well. He doesn't notice how she hums a little louder when his fingers touch a screen or that she tries to keep the area under his feet warm when he is on the bridge.
After a time she despairs of ever having him know how she feels. He still talks to her, but it is the same friendly talk she is accustomed to. She hears stories of his home in Russia, his sisters, and his life before he met her. He tells her about his roommate and his ex-boyfriend and his theory about the practical applications of quantum warp theory. She tries to express her feelings to him by finishing his calculations before all the others, by adjusting his replicator so that it produces hot chocolate with a higher cocoa content than is allowed by regulations, by blanking communications to his quarters on Sunday mornings so he gets two more hours of sleep than normal, but he doesn't seem to notice a thing.
She loves the times when he whispers to her in other languages and when he tells her all the different ways that she could be traveling which are less efficient but potentially more interesting. She loves how gentle he is when giving her any kind of input. She loves the way her sensors depict the way the light shines off his hair.
She hates the way he still talks to her as if she couldn't understand. As if she were just a friend and a mute one at that.
Briefly, she wishes for a friend with whom she could discuss her crisis of heart, but she has not encountered another one like her since the Narada, who was something of a bitch and hadn't been one for deep conversation at all.
After several days of pining and quite a few more of near suicidal depression in which Scotty spends his time stroking and cajoling her and promising her a pile of new dilithium crystals if she'll just tell him what's wrong, she decides that something must be done.
What she knows now is that she will make Chekov understand her feelings, by any means possible.
It's not exactly easy to tap into the transporter matrix without the help of a crewman (and without alerting the technician on duty) but she manages to do so with a little flexing of her nacelles and a great deal of determination. Manipulating the replicators is much easier now, since she has been mildly adjusting the quality of the food produced for a number of crewman, depending on whether they had pleased her or annoyed her in some way. She knows there is a small holographic device in Spock's quarters and she makes sure his back is turned when she transports it from his table.
It takes days of preparation, and her concentration on her task leaves her distracted from the work she would normally be doing. There is a minor power failure on Deck 5 as a result, but as far as she can tell it bothers no one, other than Sulu and the engineer assigned to solve the problem.
It is all worth it for her when she beams Chekov from his post at the bridge (when nothing important was going on) to the doorless room where she had prepared her surprise.
There is a small black table, festooned with rose petals, a single lit candle at it's center. Soft music floats from the speakers she has placed in the corners of the room and the scent of freshly replicated pie drifts from a covered dish.
“What?” Chekov says, in clear confusion.
She activates the hologram device, allowing him to see the form she's chosen. She wears a Starfleet command uniform and thick non-regulation tights (she's never been a fan of the short-skirt, no-pants business). Her long brown hair is in a bun at the base of her neck and she has settled on a pair of light, wire-framed glasses.
“What?!” Chekov says, glancing around the room, taking in all around him.
She mouths his name, wishing she could produce any kind of sound through the device.
An crease forms in between his brows (too cute for words, she must admit), as he tries to understand his sudden change in circumstance.
For a moment, she believes he will not recognize her in her new form and her warp core pulses with the agony of it.
But soon enough, his frown is clearing and his eyes take on the same awed glow she has seen when he successfully calculates something impossible.
He mouths her name.
She responds in kind, smiling past tears as he begins babbling about impossibilities and sentience and how he knew his replicator was better than Hikaru's.
She gestures for him to sit, blushing at his enthusiasm.
The Enterprise and Chekov share a smile over the table, their eyes meeting for the first time.