The problem is that he is putting his weight on that foot (or that side of the body). The best advice up here that I see is to lean on him. If that doesn't work (some of the more clever horses won't budge if they don't want to) then slightly pull them forward (or backward, depending on which foot you want to access) by the lead rope/cross tie chain - not much just one foot. This will make them shift the weight up/down.
This is easiest if you have a helper for the first few times until the pony gets the idea.
If even THAT doesn't work (or if you are alone and just can't keep his weight shifted until you get to his feet), then to get him to pick up his front feet, there is a simple trick :
Using YOUR feet, just tap him right above the heel on the tendon. He will move the front feet a step forward, and the weight shifts off, pick up the foot.
Once the foot is up, just hold it there, for as long as you can but make sure to drop it BEFORE he leans back in.
You mite get only 1-2 seconds at first, but that is ok ... keep doing on the same foot over and over again, until you can manage to keep it up for about 5 -10 min.... once you get one foot squared away the others should be easier...
Of course I am assuming you know the horse and all this is safe to do with him.... If he is particularly shy/scared/hurt etc, please find professional help outside the forum
Sorry to make it sound like a big deal, but I once groomed more than a dozen horses and had to teach many of them (Esp. Babies) to pick up feet..... so I am well aware of the angst !! Hope this helps..