As stated into the main portion of the game's page, there are eight potential candidates for growing a relationship with. Each man will have their own lives to lead however, and so in order to get close to them you will need to become an active member in their daily affairs, this means helping them with various chores around their homes.
After every 3+ tasks (not counting any fights to defend them and their livelihood) there will be a special scene between you and said character, what happens then will be determined by their specific lifestyle, though do beware that some of these men have hidden pasts, the likes of which may prove fatal to you if you are not prepared, so equip yourself as well as you can before attempting to grow closer to them. The truth behind many of these assaults will only come after you have grown deep enough into the relationship, though sometimes the mystery will simply linger as a question of perspective.
Once you have spent enough time with your choice of romantic option you will get a chance to become intimate with them, or close enough to it in some cases. With that said, some of the characters will need for Lance to be at a certain low level of purity to even get a chance to get close to, but beware of becoming too impure, as this can change the ending of your game.