My phone shows headphones are plugged in when they aren’t what is the best way to clean out the headphone jack ?

I haven't ever done this, but either method should work. Personally, I'd try the air can first as that's the least invasive option:

• Air can.
  It's simple: use an air can to blow out dust and lint that may have accumulated in the hole of the headset jack.
• Q-tip.
  Carefully insert a dry Q-tip in the headset jack to clean it out. Be sure to do this gently so you don't cause damage to your device.

https://support.apple.com/en-us/HT207532

Specifically, it's recommended NOT to use compressed or canned air

https://support.apple.com/en-us/HT207123

Good to know thanks. I've never had to clean out a headphone jack on any of the iPhones I've owned which had them.