If two people own one thing, put the possessive apostrophe after the second name.
Chet Huntley and David Brinkley’s evening news program ended in 1970. 
[this was a co-anchored news program]

If two people own different items, put the apostrophe after both names.
Dave Letterman’s and Jay Leno’s TV shows feature comedy and guests.
[these are separate shows on separate networks]