In order of importance (IMO):

1. Make sure your bike fits properly, if you have to reach too far for the handlebars no amount of core strength will prevent this problem.

2. Avoid the "death grip", locked elbows, kinked/dropped wrists, etc. Keep your wrists reasonably straight and light. Hold your body up with your core trunk muscles, don't just plop on your hands like a sack of potatoes.

3. Change hand position every few minutes.

2. Good padded gloves and possibly handlebar tape or "bar phat" can help with tingling/numbness on long rides.