Well that is a pretty big question.
I'm probally not the right person to answer that question, because I have been playing D&D since it came in that red boxed set (with dice and everything) and have been all the way through AD&D (1. and 2. ed) 3rd ed. 3.5 and Pathfinder as well as a lot of other RPGs. But here is my 0.05$
The best way to learn any RPG is to have a group teach you - never be afraid to ask. From experience I know of a lot of groups that have been happy to teach their skills to newcommers. But I guess that is not an option since you write here.
You say that you know some of the basics so some of this will be known to you.
The most important rule to remember:
#1. Roll a d20 and add something. If your roll is high enough you succeed.
Combat
Lets take the basics of combat - forget everything about suprise, grappling etc. JUST BASICS.
A combat is started by roling initiative (rule #1)
The combatant with highest initiative roll acts first and so on.
A combatant can make one of the following:
Full round action
Move and standard action
Two move actions
(you can also combine in free, immediate and swift actions - but lets forget those for now)
There is a list of different actions in the rules and if they provoke attack of oppotunity (AOO) (more on AOO later)
The most basic action to do in combat is attack. To do that you use rule #1 (adding attack bonuses vs. targets AC). For characters with less than +5 base attack bonus (BAB) these attacks is almost always standard actions - but if you want to make more attacks (two weapons, +6 BAB, etc) you must use a full action.
You can also cast a spell in combat.
In the spell description you find how long it takes to cast a given spell (standard most often). The effect of the spell is described in the spell description.
The fireball spell does 1d6 fire damage per caster level - reflex save for half damage. This means that a level 5 wizard does 5d6 damage with this spell to everything within 20' radius unless the targets make a save (rule #1)
AOO
Many actions provoke attack of oppotunity. This means that you do not defend properly when doing this action (casting spell, moving in certain ways, etc.).
If you make an action that provokes AOO and an enemy threatens you - that means he is holding a melee weapon and is within reach (5' for most human sized enemies) - he gets a free attack called an attack of oppotunity before you can make that action. This attack may disrupt your action (spellcasting) or just be annoying.
When all participants in the combat has had their turn, the combat round is over and a new round starts. The characters keep their initiative roll.
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That was the most basic of the basics. But like I said the best way to learn the game is to play it.
If you don't have anyone to try the rules with I suggest that you make two level 1 fighters (forget skills and names - just basic fighters) and let them fight a few combats against each other. In this way you get a feel for how combat works. Then you can slowly start to make tings more complicated - feats, movement, combat maneuvers, other classes, more combatants etc.
