If you just want to replace the post, then either: a) cut if flush and relocate your new post 2-3 feet on either side to clear the old concrete, or b) dig the old post out of the ground, concrete and all. If you are removing more than a few posts, you might want to consider getting a tool like an Oz-Puller. It looks like a dolly with a winch on it and can make the job much easier.

If saving the wood is your goal, then your best bet would be to cut it flush to the concrete and save the part that hasn’t been exposed to ground moisture.

You don’t. You either remove the whole thing (wood and concrete) or you leave it and dig new holes next to it.

edit: I meant leave the concrete and cut the post at base.

Your neighbor used redwood? Wow! Cedar or treated lumber is more common.

There really is no easy way to yank a post out of concrete. Best thing to do is grab a come-along and ratchet the thing out (attach it to a solid object like a large tree. Do not use a car bumper). The set your post in the hole created and pour new concrete around it.

cut it off flush and use a hammer and a good heavy wood chisel…