1. how does one go about locating an existing partnership

Only way to do this is ask around at all airfields that are close enough for
you, and post flyers in FBOs and clubs. You can also search on the
internet, but I didn't have much luck that way. Oh, and join the local EAA
chapter.

2. in the absence of existing partnerships, how does one recruit
others to go in on a plane

See answer to #1.

Also, don't discount another situation: you find a sole owner who wants to
sell you a share in his aircraft. Often there will be guys who own a plane
and don't use it as much as they thought they would. When they hear you are
looking, they get to thinking about it, and realize a partnership could be a
good deal for them. That's how I found a partnership.

3. any advice on buying the plane outright and selling part interest
in it to others

I'd avoid this, for 3 reasons. First, you've got no guarantee that you'll
find a partner after you buy. Don't do it unless you're fully prepared to
be a sole owner long term. Second, arriving on an agreed-upon value might
be difficult. The prospective partners aren't going to care what you paid,
only what they think it's worth. You might wind up eating a loss. Third,
if you comply fully with sales and use taxes, you might get hit twice; once
when you buy, and again when you take on partners.