How do I apply for private health insurance if I am 68 yrs, retired, and do not have Medicare.?

Can you buy into Medicare? That might end up being cheaper than buying insurance under the ACA plans in your state. The annual deductible is $183 Part B and $1400 Part A this year. What have you checked so far as insurance plans go?

You can purchase a bridge plan.

You apply same as anyone else.

Sure you can apply.  But it's likely to be much more expensive than Medicare.  Why would you not apply for Medicare??  Do you not qualify??

My state (California) has a website you can go to, answer a few questions, and they submit it to every insurance company in the state, who will then mail you offers with the price in them.

Use a tongue depressor or popsicle stick, so you'll have something to bite down on when you see the cost.  If you aren't part of a group (like your employer), private medical insurance is just outrageous.

Why don't you have Medicare?  If you worked in the US for at least part of your life, you've already paid for it!