If possible, ensure that the start and end of the selection are at moments of silence (or near silence). Because the audio is being stretched the stretched waveform is unlikely to match up exactly with the original waveform, and thus cause a click.
Note also that the “Sliding Time Scale / Pitch Shift” effect is a more advanced “stretching” effect that will usually give better sound quality than the more simple “Change Tempo” or “Change Pitch” effects: http://manual.audacityteam.org/o/man/sliding_time_scale_pitch_shift.html
Also, the “Sliding Time Scale / Pitch Shift” usually manages to avoid clicks at the start, so you only need to worry about getting the end of the selection click free.
Whole phrases are easy to work with, and in spots where I need to adjust just part of a phrase, I’m using the ‘generate silence’ function to make a tiny space, adjusting the tempo as needed, then deleting the silence and using the ‘draw’ function to tidy it up.