you have to find one firstly. Then you have to get the owner to agree to letting you fly it:)
as to what you need, i wouldnt be surprised if you needed both PPL, instrument, and multi-engined licenses. good luck with it, someone else may know more though.
As to how long. Do you have any leads as to an owner or company that has one? where are you from and what level of flying are you at.

I live in Sevierville, TN.
There is a company in Morristown TN (about 40mi) that has a few DC3's.
They all are working birds and are hired often. They offer training there, but be it a Sunday I can't contact them.
At the present I have logged 25 hours but I probably have flowen 100-150 in various aircraft (anything I can Cessna-taildragger-warbird) not logged.
I just never thought of getting my own liscence until this year. Don't ask me why!
I have been fortunate that the pilots at Gatlinburg-Pigeon Forge airport are such nice people, and don't mind treating me to a flying lesson in their airplane so most of the flying time I have has been without a CFI so those hours don't count. At least to the FAA, but as far as I'm cocerned they count to me and I don't need a piece of paper from the FAA proving that I know what I'm doing! But in order for me to be able to go out on my own or take along a friend I need one, so that is what I'm doing.

Spent a lot of time in the DC3 and the DHC-3
For the DC3 (DAK) you require a multi-engine rating.
To be hired by an airline you will also require an instrument rating and current medical certificate.
The aircraft itself is really a two pilot aircraft because the cowl flaps are to the right of the co-pilot.  The landing gear handles and flap handle are also easier to reach by the co-pilot because they are to the left and down from his seat.  If you have wheel/ski combination that is also easier for the co-pilot to do rather than the left seater. As for hours and time depends on the company and their insurance.   Keep the Dream

Ah yes, forgot about the insurance requirment!!
Finding the DC3 isn't hard, there are a few within a 40 mile radius of me.
The operating cost are another thing. I don't think I want to buy one, at least not yet, though I do know where one is for sale close by.
In Morristown TN, they have a fleet of DC3's and they offer training in them. If I'm not mistaken for a three hour training course, preflight and then the GRAND FINALE runs about 3G's!
I'm going to contact them tommorow to get cost and I'll let you all know what i find out.
My main goal is to fly one once even if it is just for a hour or so. And that I will within a year!
Thanks to all of you for the replies and support and you can be sure that photos will be posted when my dream comes true!

"BTW, are there any DC-3's left in commercial service?"

Yes the ones they have in Morristown, TN that I refered to are used on almost a daily basis for hauling everything from people to cargo, it is a small private company that if I remember correctly has a fleet of 10.
Also how is that you guys copy a quote from a listing and paste it to your post so that it is boxed in grey?

DC3 are old but still in service! That's cool, I would love to fly on one of those

Redwing,
I doubt I could do that since my eye vision isn't very good. Does DC-3 fly to KLAX, KDEN or KSFO? I was wondering if I people today can actually fly on those as pax. What company still own those? I know for sure, United, or Delta no longer use those.