How do you insulate a ceiling and finish it on the inside with wood?

It probably is a job for professionals unless you have building experience and the necessary tools and equipment needed. I am assuming it is a cathedral ceiling? Along with a miter saw, compressor, and nail gun to name a few basic tools you'll need, you would likely also need scaffolding for a job like that, which of course can be rented if you have the know-how and desire to undertake this job yourselves. 

The first order of business is making sure that what you build it properly for your climate - where do you live or what climate zone are you in?

To clarify - currently you have no insulation whatsoever? I'm just not sure what you mean about having 'no insulation from the inside'. If you're house was built in the 50s and depending on your climate zone, it may not have any insulation. and depending on the climate, it may or may no need a vapor barrier. 

And it sounds to me like you have something of a timber frame ceiling at least, which would give you room to insulate between the purlins or rafters. The remaining questions I'd have would be if there is an air barrier and or a vapour barrier. But yes, you could finish it with wood afterwards, and here is a link to a page that may help for choosing a wood type, it is about Installing Wood Ceilings & Cost compared to Drywall. You will see several types of wood, I think the lightest may be birch or maple, but maple can often come with some beautiful but dark streaks through it. In my opinion, those woods would give you a more modern look, while pine tends to yellow a bit overtime and would be a bit more traditional there is also the option of doing something like an opaque sort of milk paint, which can still show the grain but lighten the wood quite a bit, you will see examples on  that page link above.  Feel free to write back with a few more details about how it is built, where you are located and if there currently any insulation, and we may be able to offer more help in choosing insulation and how much to install.