Hey Sakuraburst!
I use Ableton so I usually start off with experimenting with some timestretching/warping in complex pro mode. I love to use a multiband distortion plugin called Subvert for mangling the sound/saturating it. To add movement, I stack a bunch of autofilters and automate their frequencies. I put glue compressors here and there to squish things and pronounce different movements. Additionally, I like to add a super short decay Ableton reverb with a small room size and the spin near the top right...adds some really interesting movement. Also, I regularly add extremely short decays with a medium feedback to add a metallic quality.
Depending on the sample, I may import it as a waveform inside of Serum and play around with that.
Here's a three clips of what my process was like on this instance of an ambient growl:
https://soundcloud.com/safeko/sets/the-bug-sound-design/s-r0As5First clip = timestretched sample from an FM patch I made in Serum.
Second clip = reversed and lightly processed
Third clip = Subvert effect patch dry/wet automated, vocoder dry/wet automated, saturation drive automated, reverb decay and dry/wet automated.