a) Clearing my mind - I usually do this when something existential consumes me i.e. I get a bad phone call, someone pisses me off, anxious and unfocused, hyper, etc. and I simply can't stop thinking about it during the day. I do very controlled breathing exercises for 20-30 minutes. Inhale for 5 secs, exhale for 5 secs;then 7 secs;then 10. In almost all situations this frees my mind from being consumed. In the most drastic cases I've had to do this for nearly 2 hours. I'm almost always drenched in sweat and feel revived afterwards.
b)Relaxing my mind - I do this when I've had a very long day tired, but unable to fall asleep for various reasons. Again, controlled breathing for the first 15 minutes. The first few weeks were extremely tough. My mind would start racing in all sorts of directions and was unable to be mindful of the breath, especially since I was not consciously counting. After the first 4 weeks, though I was able to 'push' thoughts out of my head and start relaxing certain muscles in my body. I really can't explain this process/feeling without sounding like a crazyman, so I won't. But I'm at a point now where I can almost feel as though my mind is a shell and I can consciously shed layers off with each layer giving me a new sense of calmness. This type of meditation is vastly different that the one before because I'm here I'm not fixated on one certain thought, my mind is just kind of loosey-goose.
Disclaimer: I was taught meditation by a Daoist monk, so if there are any religious undertones, I apologize. Its unintentional.