I have done a bit of transcribing and use Transcribe ! software which is brilliant in every way. It helps me enormously.
My sense of relative pitch and my ability to translate rhythms from their sound to their notation and vice versa are not good at all, but I think it is worthwhile trying to get every aspect of the transcription right (key, harmony, pitches, rhythms, articulations and effects). You can always go back and refine your transcription later on.
Here is a rough outline of my transcribing process (I use Transcribe! and Sibelius simultaneously open), but you can do it onto paper or whatever you want.
Get the version of the tune that you want to transcribe (er, obviously !) - that might mean capturing it from YouTube or...