I have a Nikon D5100 and some beautiful old Cosina lenses (completely manual) What sort of adapter do I need to buy to use these lenses?
This depends on what kind of bayonet or screw those lenses use to mount on a camera. Basically you should look for xxx to Nikon F adapter, where xxx is the mount type used by the lens.
You will likely need a correcting lens adapter, since the Nikon has the longest flange distance of any camera manufacturer and focusing to infinity becomes practically impossible. This will affect the image quality, and more often than not make it worse than intended. See more here: How will old M42 lenses work on a Nikon camera?
If these are Leica-M mount lenses, then you cannot adapt them to any dSLR mount. The registration distance (how far away from the image plane the lens has to be held) is much smaller with rangefinder lenses than SLR lenses. You'd end up interfering with the mirror path if you jammed the lenses far enough into the camera for the lens to achieve focus to infinity. They will easily be adapted with simple rings, however, onto mirrorless cameras (Sony E-mount, Fuji X, micro four-thirds, Nikon 1, etc.)
If these are Nikon F mount lenses, you don't need any adapter at all. You just need to set your camera to shoot with non-CPU lenses. Be aware, however, that you will not get accurate metering with a D5100.
If these are Canon FD or Pentax K lenses, you'll have to use an adapter with a glass element in it to act as a short teleconverter so you can achieve focus to infinity (not sure about M42, though--you may be able to find a simple ring adapter. Maybe not). But, it'll be like having a teleconverter on the lens (lose some max. aperture, gain some focal length and probably a little softness).
See also: Can I use lens brand X on interchangeable lens camera brand Y? for more details.