Updated: May 28, 2020
If you want quick results then the best point to start from to alleviate anxiety from my experience is not meditation but breathing exercises, the “abdominal breathing” not the usual one. Fears and anxiety tend to gather in the lower part of the lungs and large majority of people practically never breath from that part (lungs volume is about 5-6 liters on average and we inhale/exhale just 0.5 liters on average - the tidal volume).
The pranayama techniques for instance try to deal with these, but there are many other breathing procedures alike.
Breathing will alleviate for the moment your anxiety, but you still need to find out the Cause of it and release it, and the Cause is in you.