The biggest consideration for addressing wrist and hand pain (especially when riding long distances) is by reducing the pressure you're bearing on your wrists. Aggressive riding postures put excess pressure on your arms/hands/wrists/elbows for the benefit of aerodynamics and better advantage on your pedal strokes. For the majority of cyclists unconcerned with such things (tourists, especially) comfort and rideability are more worth the effort.
The traditional KOPS (knee over pedal spindle) has been the go to rule for adjusting saddle fore-and-aft for quite a while. Lots of people find it totally satisfactory, however, everyone is built differently and quite often different riding styles necessitate different setups. Moving one's weight back onto their sit bones and feet (two parts of the body that aren't as sensitive to bearing weight) will in turn reduce pressure on your wrists. Your saddle needs to be adjusted for the appropriate height and then set back a bit.
The idea is that when you squat (sans bicycle), your hips have to move back to balance your upper body. In the above diagram, you can imagine the effect of moving your saddle back as being a similar shift in weight.
To compensate for that more upright posture, you may need to change your stem and spacer orientation and setup. The idea is to bring the bars up and back (with some room for fine tuning.) Most touring bicycles are fitted with tall stems that enable you to achieve this posture. If you're refitting a bike, you may need to buy a new stem or some spacers.
Many people will suggest adding padded bar tape or thick gloves. While this is a great way to relieve some of the roughness and pressure, no amount of padding will make supporting your upper body all day comfortable. The idea is to use your legs and rump to get you from place to place.
Also, these sorts of issues can certainly be caused by medical complications (carpal tunnel syndrome, especially), so consult with a doctor if things start to deteriorate or worsen.
Further resources can be found at SheldonBrown.com and RivBike.com (and many others.)