I’ve declared a non-flying attacker, and my opponent declared a flying blocker. When combat damage is dealt, I deal damage as normal, but can the damage dealt by the flying creature be absorbed by my non-flying creature, or do I have to absorb it with my life?
It's your turn and you are attacking your opponent; that means you won't lose life from combat damage. The flying creature will deal combat damage to your non-flying creature. The fact that it has flying has nothing to do with it; that just determines whether it can block or be blocked.
Everything you need to know about this is covered in the basic rules; look for the section 'ATTACKING AND BLOCKING'.
- An attacking creature that is blocked deals damage to the creature or creatures that are blocking it, and vice versa.
I think you may be a bit confused between magic and Yu-Gi-Oh rules.
Using your example, you declared attackers and your opponent declared blockers.
Your creature does not have flying so it can be blocked by any creature (unless stated on the creature itself, either attacking or blocking for example Skywinder Drake).
In this case, the ability the blocking creature has is irrelevant.
Abilities that will usually matter when defending (keyworded abilities) are for example: First strike, double strike, last strike, deathtouch, lifelink, infect, whither and indestructible.
In the case of the attacking creature the above abilities are also relevant, but one of the most relevant regarding damage will be trample as mentioned on other answers.
If your attacking creature's power is higher than the blocking creature's toughness then your attacking creature would deal enough damage to the blocking creature for it to be lethal, and you could then assign the rest of the damage to the defending player. Attacking player "always" chooses how the damage is assigned to defending creatures/players according to the rules. The only instance where a defending player gets to assign damage and "blocking order" is if he controls a creature that allows him to block more than one creature at a time. The defending player can never "trample" damage to its opponent as such ability does not exist and they are not the attacking player, therefore all damage must be assigned to the blocked creatures.
If there is no trample (or any other abilities involved) combat between creatures will never cause damage to players.