Instruction:
What is the best way to approach a new cat?

Response:
First, it's important to know the background of the cat.  If it is a stray, you might want to keep your distance since you don't know its vaccination status.  If it is a known, healthy cat, then you can approach it.  Do so with care so that you do not scare it away.

There are several techniques to make yourself more approachable.  Ideally, the cat will approach you; you will not approach the cat.

Make yourself look smaller.  Crouch down, and do not look threatening or overly anxious to approach the cat.

Try the "slow blink."  Look at the cat and slowly close and open your eyes.  Also try looking away lazily.  If the cat respond with its own slow blink, that's a good sign.

If the cat comes near, try offering your hand down low, with the palm turned down.  Hopefully the cat will come to you and rub against the back of your hand.  If so, then you can try petting the cat more actively.