Toono Shiki hears of a new series of murders in Misaki similar to the ones that took place in Tsukihime. Whilst searching for the murderer he meets Sion Eltnam Atlasia who initiates a fight with him, attempting to capture him. After the fight she reveals that her reason for attempting to capture him is to get in contact with the "True Ancestor" (referring to Arcueid Brunestud) so that she may acquire information on the "cure for vampirism". Shiki then decides to help her with this task.

[Edited from Typemoon Wikia]

Melty Blood is a 2D fighting game. The first couple of PC releases (up to Re-ACT) had visual novel style story modes with multiple endings and a secondary story mode in the arcade mode. Later versions (from Act Cadenza onwards) do not have proper story modes like previous incarnations, but they add more characters.