Monte Cook made it a point to design 3e to be agnostic about using miniatures—groups could use them if they preferred, and groups that didn't could play just fine too. He wrote an article about it ages ago: "Running a 3E Game Without Miniatures". The 3.5e update moved much more strongly toward "you should use miniatures" than 3e did, but the basic techniques he outlines for managing miniature-less combats still apply. (I'd say they even still apply to 4e with some careful thought about the tactical needs of that system, but that's not a can I'll open.)
The quick summary is that there are four features of combat that have to be handled differently when minis aren't giving them to you "for free":
- Attacks of Opportunity
- Line of Sight
(I'd argue that the fifth is a clear, shared understanding of the environment in which combat takes place.)
To play without miniatures, just be mindful in your descriptions about how these features of combat are either in play or not. The thorniest, Attacks of Opportunity, is handled like this in the article:
When in doubt, give both NPCs and PCs the benefit of the doubt. If a fighter backs up (a 5-foot step) away from the bugbear he's fighting to drink a cure moderate wounds potion, don't worry about whether he backed into the threatened area of the bugbear fighting his friend. He didn't.
This method takes a bit of an adjustment from players and DMs both. To manage these narratively the GM has to describe the surroundings clearly, filling in blanks as they're discovered, and be ready to resolve ambiguities generously. The GM has to keep track of the position of the PCs and the intentions of the players so that actions can be resolved smoothly.
Players, for their part, have to become more descriptive too. No longer is it enough to think tactically in silence and then move a miniature to the perfect square—now players have to describe what their character does and to what purpose, and the more descriptive they are, the more obvious it is what their PC will be a position to try in reaction to the next unexpected turn of events occurs.
One objection players can have about playing without miniatures is that it robs them of the ability to play tactically. Not so! The difference is only that instead of moving a piece of plastic into position to take advantage of some tactical rule like AoO, you are setting your character up to take advantage of the rule by verbally manœuvering them. All the articles examples are about narrating how advantage is about to be gained. For AoOs, the article gives the example:
"I'm going to stand right by the door so that if anyone runs through it I'll get a free attack as they go by." Now it's not 100 percent important where the character is standing. You just simply know that if someone runs through the doorway, they get whacked.
"The dire rat moves around to flank you with the dire rat you're already fighting," you say. It doesn't matter where exactly everyone's standing – just that the character is being flanked by two rats.
For line of sight:
"I move until I can see the hobgoblin in the next room and fire my crossbow." All the adjudication you need to make is whether this is a 5-foot step or a move action, and that's just a judgment call.
The DM can set up tactical situations this way too. The examples for handling range are both examples of the DM creating situations that constrain what the players can do—at least until they take action to change the situation to their advantage:
"The orc archers are two range increments away."
"The two medusas are too far apart to catch in a lightning bolt."
By moving to tactical description of combat, players and DM take the work that miniatures were doing and put that job on their own narrations of the action. The benefit is a more imaginatively-rich experience of combats. In my own games I've used both miniatures and narrative combat, depending on my preferences for particular encounters, and the end effect is that months and years after the game the fights that are remembered in more detail and as most exciting by the players and myself are the ones done narratively.
And example is from a Savage Worlds game I ran. The PCs were sneaking up at night on a group of cultists who'd kidnapped a baron and made camp in a long-grassed field. Instead of setting up the grid when the PCs surprised the first sentry, I ran the fight with the sentries narratively. It was tense and exciting as the players tried to silence the sentries before they called for help. The sentries taken care of they snuck up on the camp and attacked, for which I used the grid. That was tactically interesting, but much less narratively engaging. The net result is that the fight with the sentries is the part of that encounter that the players reminisce about—it was simply more memorable, and what GM doesn't want their games to be remembered fondly?