There is a limit to what you can do-- cracks, for example, will remain.
But to rescue what you've got, here's how I'd do it:
Warm water, wrung-out sponge, go over it once (all surfaces) to remove dirt or dust.
Then neatsfoot oil with your bare hands. all surfaces. Yeah, there are other conditioners out there, but this is The One That Started It All-- the 100% oxygen for the guy turning blue, if you take my meaning.
In any case, neatsfoot goes on in thin coats. It will soak in so that the leather looks shiny at first, but then turns matte. At first, your leather will be very thirsty and will soak up the oil quickly. But look for the place to quit with the neatsfoot-- the layer where the leather stops taking up the oil within 10 or 15 minutes, returning to darker, softer but matte-looking. If the top looks fine, but the underside still seems thirsty (as can happen), give it another coat. You can over-oil, hence the warning.
With really dry leather, don't bend it too much in order to get the oil to soak in-- you will crack it. As the past layers of neatsfoot penetrate to the innermost part of the leather, you can bend it some, but be gentle.
When you have achieved the suppleness you want, or the best you think you can get, it's time to seal that in with a thin coat of glycerine or some other saddle soap with an almost-dry sponge.
There you have it.
You can come back to recondition later should your leather need more.