Player vs. PC awareness - It's in the nature of the game for players to have limited knowledge. What they do know depends entirely on the DM, how he describes a scene and how he responds to their questions and actions.
Their characters, on the other hand, should always be assumed to have any knowledge that they could reasonably glean from their environment.
This is doubly true in combat, where bad information costs lives, and triply true in Theatre of the Mind, where it could reasonably be claimed that a hill giant throwing boulders from the back of the fight would probably have been something the PC's would have noticed.
So make sure your players have all the information they need to make good decisions, and be willing to roll-back the round if they make a good case for it. Be generous. TotM gives you, the DM, almost all authority, so you have it in your power to make the game run smoothly, fairly, and dramatically for everyone. The best DM's exercise this power to the fullest.
Over-describe - This advice applies to everything from setting the scene to what your monsters are doing. Your players rely on you for everything. Every choice they make starts with your narration. Make it good, and you'll inspire them into heroic deeds.
Bad: "At the end of the path is a fort and stable. There's a low wall around it and also some trees to the east."This isn't useless but will just invite a flurry of questions from your players. Does the path go up to the fort? Is the door shut? How many windows are there? Can we see anyone inside? Pre-empt the questions and coax their imaginations in the right direction.
Better: "The path ends at a shuttered old fort protected by a gate and perimeter wall. It looks empty. There are hoof-prints in the mud. There is stable under the trees to the east. Hay is piled outside."This is serviceable, with enough description to invite the right questions. You can bet the rogue is already planning to use the wall and/or the trees for some recon, and signs of life near the stable suggest all is not what it seems.
Best: "The path ends at a rusting gate set into a three-foot perimeter wall around an old fort. The windows are shuttered and there are no obvious signs of life. One shutter hangs off its hinges, banging in the wind, revealing a broken pane of glass and darkness inside. The perimeter wall is a couple of feet high and in good repair. Hoof-prints are clearly visible leading through the gate to a small stable which sits in the shadow of a copse of trees to the east. Hay is piled outside. Low branches scratch the tattered slate roof."Now we're getting somewhere -- in fact it might almost be too verbose! More words does not always mean better description (anyone who has DM'd their share of published adventures down the years will have tales of excessive and often hilarious boxed text), but at this point the players will be pondering a few mysteries: is the fort is as empty as it looks? What might be lurking behind the shutters or waiting for them in the trees?
These are unanswered questions, to be sure, but they're the right questions. Instead of fretting over exactly what their characters can see, the players are contemplating elements of narrative and suspense. Not only that, but the swinging shutter suggests a frontier-like atmosphere which will immediately conjure images of ambushes, gunfights, and desperate last-stands. Assuming this is what you're going for, the job is half done way before the action even kicks off (if indeed it does).
Too much: "The path ends at a rusty old gate set in a defensive perimeter wall around an apparently disused fort. Shutters hang from the windows and you can feel eyes on you from behind the broken glass. Two sets of hoof-prints, less than a day old, lead through the gate and to a stable. Fresh hay, stacked after the recent rain, stands in the sun."How much is too much? In this example, words like "defensive" and "apparently" are too on-the-nose. Phrases like "...you can feel eyes on you..." should be avoided at all costs; it's never a good idea to tell players what their PC's are feeling, and besides, you want your players to actually be feeling that eyes are on them. The only way to achieve that is to invoke it through description.
As well as that, the description also neutralizes any opportunities for ability checks, which are bread and butter when it comes to PC's and how they interact with the campaign world. In the example, the DM has obviated any need for the Ranger to use his Wisdom (Survival) check, either on the hoof-prints or on the pile of hay, to see how old either of them might be. Not to mention he's all-but hung a neon sign on the fort warning the PC's of a possible ambush.
Anticipate - Your players will ask you questions. When they do, anticipate their plans and contingencies, and you can answer some unasked questions as well. Essentially, always give them more than they asked for.
Even though everything is happening in your collective imaginations, you, the DM, will have much more information at your fingertips. You might have an encounter map, and you'll definitely have creature stats, positions, goals, and strategies. Get as much of that information into the open as you can without ruining the encounter or going too far and suggesting courses of action which the players might prefer to have come up with themselves.
"Can I reach the kobold sorcerer in one move?"Range and positioning - Feet and inches are all-but irrelevant without the battle-mat. Describe, don't specify. If you use feet or squares to describe distances, you're likely to cause trouble for yourself later-on when players start adding movement rates or spell ranges to the arbitrary numbers you quoted, and question how certain monster actions are possible and how their actions are not.
Better: "Only if you run, which will mean some penalties while dodging the spear-men."
Best: "If you run, you can make it but will be at the mercy of the kobold spear-men. There's a tipped-over book-shelf between you and him, but you know there's a kobold hiding in the shadows over there somewhere."
The goblin is not 5-feet or a square away, he is next to you.
The bugbear is not 15-feet away, it is out of reach.
The coffin is not 20-feet away, it is nearby.
The tree is not 50-feet from you, it is far away.
The archer is not 250-feet away, he is at long range.What will happen is that you and your players will develop a short-hand for how many moves it will take to reach something, and more than that, whether it's worth even trying.
If you or your players are not prepared to abstract distances in this fashion, it may be advisable to use a battle-mat after all. Removing all doubt over range and positioning is what the battle-mat does best.
Proximity - Players really only care about a few specific things:
Whether a target is in range. For melee attackers, this means "Will I have to move in order to attack"; for ranged attackers, this means "Can I hit him without Disadvantage?"
Area of effect spells. This is one of the most difficult aspects of TotM and can often lead to problems. It's one of those occasions when pushing just beyond reasonable character knowledge can save a lot of headaches. Forestall disputes by dealing in absolutes and providing options.
Player: "How many orcs can I hit with my burning hands?"
DM: "From behind the altar, half of them. If you risk a move across to the fountain, you should be able to get all of them, but the chieftan is likely to get cover from a nearby table."
Attacks of opportunity. In 5E these are drawn when leaving a creature's reach. Your players should never have to ask you this; always tell them when a move will attract an opportunity attack.
Concentration. If a caster is concentrating on something or Ready-ing an action, they might be interrupted by damage or some other effect. Players should be expected to maintain a decent level of awareness about their PC's proximity to potential threats -- that's just a natural result of paying attention, after all -- but as their turn comes up, it's often worth zooming in for a close-up of the action, even if you're about to reveal what action your monsters are going to take.
For example, you might tell a player this just before their turn: "Now that your fighter Rejik is down, you see two of the kobold spear-men turn their attention to you and run their tongues over their teeth." This increases the tension and gives the player a lot more to think about than where the next fireball is going to go. This also falls under Over-describe, and will help keep the action fluid at the table.
No-one is going to care if a monster or PC moves a little bit more than they should have in order to get to the action. In TotM the exact distance between combatants is utterly irrelevant; it all comes down to how many moves a PC has to use before he can get in range. In a game where most people have a free 25 or 30-feet move built into their action, does it really matter if it would actually take 1.25 move actions to get there? Just get them there, and keep the action moving.