Filtering on a time signal
My signal is a time-signal (displacement vs time), but the filter takes the input in terms of cut-off frequency. Does this mean I have to convert the signal into frequency domain, or does the filter take care of it? I am bit confused on how this actually works.


You design or specify the filter in the frequency domain, but the actual filtering can be directly accomplished in time.  There are FFT based filtering algorithms that are typically more efficient, but there is no requirement to transform your signal to the frequency domain.


On a related note, I don't know the frequency of each motion that I am trying to filter out i.e. the intuition is that the frequency for different motions be different, but how do I determine by cut-off values? Is it usually done by trial and error, or is there a more scientific way to accomplish this?


Anything that doesn't require trial and error is suspect, scientific methodology wise. I suggest that you try to be more specific about what filtering out different motions actually means.  Some kinds of phenomena are a superposition of features which are often separable, of which some can be "filtered out" and others don't lend themselves to that. 

You might want to use a tool known as the Short Time Fourier Transform (STFT) and see if you can eye ball any patterns associated with desired/undesired motion.

Finally, try Google Scholar.