I'd like combat to flow like this, very descriptive: "I attempt to duck under my foe's flat swing, crouching at the knees, swinging with all my might to drive my axe into his hip."
That's the kind of description that happens for attacks in my game. I don't have many rules - fewer than regular d20 by far. I use a heavy load of DM adjudication to get around it.
The system is pretty simple:
1. Player describes PC's action - Just like your axe swing into the guy's hip
2. DM assigns modifiers - Here we'd add any modifiers for STR or DEX, proficiency, crouching down and exploding into the guy's hip with your legs, and having to dodge under his blade (as well as any defensive mods)
3. Roll is made - d20 + modifiers, at this time your action is locked in, you can no longer change it
4. Action is resolved - We resolve
the action your character takes; that's probably the biggest thing
After the roll is made, if your roll was successful (you met or exceeded the DC), then you crouched down and drove your axe into the guy's hip.
At this point I'd stand up and physically show how the two of you are tangled up with each other. Since you ducked under his blade, you should be right in his face, eh? He'll have to do something like smack you in the head with the pommel of his sword, or draw a dagger and stab you in the face, You can continue with your attack's follow-through and push him to the ground (with a bonus), twisting the axe in the wound.
What you said happened, happened, and now we move on from that point when deciding what actions characters can take and what modifiers are applied to rolls and DCs.