Action Movies
The easiest source of material is action movies.
How many action movies have fights in empty rooms or flat empty areas? Not too many. Action movies always have fights where there are things to climb, knock over, break, set on fire, knock someone over/into, sharp things, burning things, things to fall off of, etc.
Whereas in a grid based game, you'd be looking where to place these exactly and how many squares, and so on, here, you're just going to draw a very sketchy map and write down some easy items that might come into play.
Castle Hall Example
A smaller greeting hall, with a couple of round tables and chairs.
Shuttered windows w/o glass - someone can be pushed out of these for a 50' fall.
Tapestries - can be pulled down and over someone to entangle/blind them
Braziers filled with hot coals - push someone into them, knock them over onto the ground
A serving tray - can be used as a temporary shield against ranged weapons, or thrown
Stairs - the hall is entered by stairs leading down to the central entrance and exited by stairs up to the high landing. it's about 20' of stairs either way, great for a tumble if you want to push someone down.
Display Armor - two suits of armor stand on display, they can be knocked over or used as cover.
You can get to the point where you don't even have to list everything out like this - you might write down 6-7 items and know how to improvise what they do, or pull up an image of a location on the internet and use that as reference. Or even a sentence for a movie reference ("The grand cathedral from Castle Cagliostro") as shorthand for yourself.
More than Decorations
So, you've got all this stuff, right? And often enough in a game, players will ignore it if you don't give it some mechanical value. An easy way to give all this stuff some value is to give it bonuses to hit, bonuses to defense if you're hiding behind it, or some kind of penalty or stun to the enemies if you use it upon them.
If the object can only be used once, I generally like to slap a +4 to hit on it and significant damage and/or stun... enough the players will seriously consider it in favor of just using their weapons. "Used once" applies to things like "knocking over a bookshelf onto an enemy" but also applies to things which any intelligent enemies will avoid after you do it the first time, such as "pushed a guy out the window".
Reusable stuff often either requires some other defensive tradeoff ("Yes, you can keep throwing barrels onto the bar area below, but you're at -4 AC when you do because lifting barrels is a particularly vulnerable position") or gives a lower bonus.
Initially, tell the players a few of these ideas - fighters and thieves are probably going to be the best to think about how to use their environment to their advantage. As players become more adept at playing, you can simply describe the room and they can take advantage of it themselves.
Hazards
Hazards are great. Aside from being the kind of thing you want to toss your enemy into, and avoid getting tossed into yourself, you can also make them shifting/moving hazards. which then forces the players to keep moving or doing things.
Hazards can also be weighted to affect some more than others. Lizardmen don't find a swamp hazardous, but they're totally happy to bear hug you and drag you under the water in your heavy plate armor. The burning building that has chunks of wood falling down is bad for everyone, but maybe the halfling can run under tables without crawling or kneeling and keep fighting just fine.
Consider what a Hazard does, consider if it can and does move, and how fast. It can be a way to push players into new areas and opens up ideas like trying to run past enemies or hold the enemies into an area while the hazard does the work.
The most boring way to play D&D
"I roll to hit. I miss." "The goblin hits. 2 points of damage." "I hit, 4 points of damage." over and over.
If the best choice in a fight is the same attack that the players ALWAYS use, there's not reason to do anything else. At which point you're playing the dice version of the card game War - where choice is irrelevant to luck.
Use the ideas above to push your play into anything BUT that. Sure, sometimes, just swinging the sword is the best idea. But many times, pushing an enemy, throwing something, knocking something over should be also great choices for players.
Also reward players when they think of using something in a way you didn't consider before - "They're trapped under the fallen chandelier? I'm casting Heat Metal!" "Oh geez, aside from the damage, I think it's time for a morale check! Too much pain is a good reason to run..."
