It's hard to help without knowing more about what you're trying to find, but I'll try to help how I can.
First of all, it is very difficult in most places to research Jewish genealogy earlier than around 1800. For example, in my places in Europe Jews did not use surnames until forced to in the early 1800s. It is thus quite difficult to trace Jewish families back beyond when surnames have been in use.
You say that your family was from Kiev, but do you know if it was Kiev the city, or a smaller town in Kiev the region? What documentation do you have that points to your family being from Kiev? I would first research this first point, making sure you know the exact town the family was from before trying further research. Perhaps there are immigration or vital records from Harriet's parents that might shed some light on where they were from exactly?
If you're sure the family was from the city of Kiev, then I would start with the Kiev, Ukraine resources found on JewishGen:http://www.jewishgen.org/ukraine/towns-gubernias/kiev/kiev-h...
and if you know the surname, you should create an account on JewishGen and search the JewishGen Family Finder (JGFF) for 'Kyyiv' which has over 5000 surnames from over 3000 researchers listed in the database. If you know the surname and are sure about Kiev being the city they were from, then finding someone else who is researching the same surname from the same city is probably the best way to get started.
You can also join the Ukraine-SIG mailing list on JewishGen where you can ask more specific questions to other people researching Jewish roots in the Ukraine.
I hope this helps.