You don't need any significant knowledge of the plot of Soul Eater to begin reading Soul Eater Not!. It is set in the same world, but Soul Eater Not! takes place chronologically before the beginning of the Soul Eater manga and mostly focuses on characters who are not important for the main plot. If you're familiar with the setting of Soul Eater (which should not require more than a few chapters of the original) then you should be able to read it. In fact, you could probably read it without any knowledge of the original, as the major concepts are all reintroduced, but I think it will be more enjoyable for those who at least know the main characters and setting of the original.
Of course, many of the characters from Soul Eater also show up in Not!. There may be foreshadowing of future events or outright spoilers connected to these characters, but I don't remember anything major getting spoiled, and most of the references are to things which occur fairly early in the manga. If you want to catch all of the references, it would be good to read up to chapter 44 (last chapter in volume 11), and possibly a bit farther, but strictly speaking that isn't necessary.