Test strips going in normal waste. Dispose of them in the same way as you would a bandaid/plaster.
Regarding lancets, it depends. As I use insulin and have needles, I get a sharps bin on my prescription. Sharps bin disposal varies around the country.
If you have no sharps bin, you can purchase your own (they are available on Amazon, for example). Or, you could put the caps on and place them in a disposable bottle/jar, seal the lid and put out with your rubbish.
The FastClix lancets are retracted into their cassette so are no risk.
Some people use needle clippers. I found lancets thicker than the clipper were designed for and still left a sharp stump so stopped using them.