How do you increase Tomoe's affection?
I only recently played through this, but in the top right (of most screens) there's the heart/H-card menu (when you click the hear it will open a screen called 'Girls Relationship'). Click Tomoe in there (though this applies to advancing anyone). Mouse over the card you want to progress.
The first card can be done as soon as you complete Yui's wood collection quest. The second card requires you to complete the first card and the quest 'Sakura Town'. The third card will appear as soon as you complete the second card, and explain how to progress. All three cards are really just 'follow the instructions', where 'talk to her' often means going into the store and clicking 'Talk', but it could also be clicking her on the street, or just visiting the store.
That should be all there is to it (as of 0.4.2).