This page explains how I run combat. It's a system I developed after spending a lot of time reading over the PHB and DMG sections on combat and initiative, and reading how other DMs run combat. I won't get into the specific details of why I think the written system is bad, but I feel it's overly complex and tends to give one side or the other massive advantages. My system tries to keep the playing field level, by spreading out actions throughout the round.
I start by rolling a d10 for each side. Whichever side rolls lower goes first each segment; however, if any individual creatures are for some reason very fast (spells such as Haste grant -5 on the initiative roll, for instance), they can break out of that d10 result.
Inside of each segment for physical actions, for the player/NPC side, higher dexterity goes first; if dex is equal, higher strength goes first; if both are equal, I will usually let the PC go before NPCs.
Multiple attacks are handled like this - if you get one attack, it goes off in segment 1. Two attacks, segment 1 and 6; three attacks, segments 1,5, and 9; four attacks, segments 1, 4, 7 and 10; five attacks, all the odd segments; six attacks, segments 1,2,4,6,8 and 10, and so on.
Spells go off at the end of the segment that their casting time requires, all basically at the same moment.
I will allow you to 'mix up' your attacks and other actions, either preplanned or as you go. For instance, If you get two attacks, you could take the first one in segment one; this means you are done with attacks until segment six, but you could move or take other non-combat actions in segment two through five. This can get a little complicated as you mix in combat, movement, spells, wands, drinking potions, and so on, but in general I will put a segment between actions counted as the time you took to get the item out and/or put some item away. Doing such can 'push back' your other attacks from when they should have happened, or cause them to be lost. For instance, if you get two arrow shots, you could take one, then put your bow away and fire a wand in segment six, but you would not get another arrow, as that 'arrow shot' uses up 5 segments of 'combat time'.
This results in me having a sheet of paper with a lot of scribbling on it, but it gets the job done, and a character with only one attack doesn't effectively spend nine segments standing around doing nothing.
Monsters typically have much simpler lists of actions, and their attacks are broken out by number of attacks into various segments. NPC foes can be as complicated as a PC in their choice of actions, and can dynamically adjust as the round proceeds.