If you have never ridden rollers at all and you're nervous about falling, find yourself a doorway. Most rollers will fit in the doorway and you want to place the rollers so that your elbows, rather than your bars, are near the doorframe. If you feel yourself getting wonky or you fear you'll tip, just use your elbow to gently guide yourself back into position.
I have used this technique with every person to whom I have ever sold new rollers, and it works every time. Then you can move to a wall, and use the other fellows suggestion of placing a chair, just in back of the bars, so you can grab hold and help yourself getting started and stopping.
Once you're a pro-- and if you ride enough you will be, but to ride rollers that much you almost need your head done in-- you can ride in the middle of the basement or the spare bedroom or what have you.
I have no trouble riding rollers but it is a workout, the drag of the tires, the friction of even the nicest rollers and the friction of the belt make an easy gear a bit of an effort and you have to pedal a certain speed or the bike will lack enough gyroscopic force to sit upright, so, unless you have paid for a set with a flywheel, there's no breaks.
A very short gear will make you pedal your arse off to keep upright, a very tall gear will let you get away with a stomper's cadence. I prefer small ring, one gear down from the middle (of a 10 speed) when I'm going, but I start a couple clicks up the cog and finish the same way. Doesn't take much effort but it will still keep your pulse up and you can listen to the sound of the tires to see how round you are. When I get tired I can hear the whoosh, whoosh of some very square strokes. Oddly enough the first place I feel sore is the back of my knees from concentrating so fully on trying to pedal circles and bringing my leg back, up and around. Almost never feel any burn in my quads. But you will also wear yourself out a bit with trying to keep a light grip on the bar. Isolating your hands from your lower body is the key, but having a quiet upper body means you need to hold your core without using your hands as much.
I usually ride for 30 minutes or so, and I put a video on so I have something to watch besides the clock. Look ahead-- if you're not watching anything look about 2 metres ahead of your front wheel and focus on relaxed, round strokes.
My only warnings are these:
I have ridden off the rollers countless times, sometimes ending up in a heap, sometimes doing alright. I get caught in my thoughts or the video or the music and ride straight off the side. The bike will come to a screeching halt. If you are set next to a wall you can sort of cheat that side and your arm should hit before you ride off. 20 years ago I put pieces of tape on the outside 7cm or so of my drums so that when I was riding near the edge I could feel the thump thump thump thump warning.
You need a fan on, but you will still drip sweat. Don't do this over carpet or the Mrs. will likely lose her mind. Also, they make a sort of sweat catching thong that goes from your bars to your seat post to keep from corroding your stem, your headset and fixing hardware into a big lump. Either grease all that very well or get a sweat catcher.
I also have a mat I put down on the carpet. Saves replacing it.
NOTHING is as slippery as cleats and a cleaned (likely waxed) tiled floor. Take care. If you hop off to fill your water bottle up in the kitchen you might end up on your arse. Polished (well-trodden) concrete is nearly as slippery.
I keep the bike in the study here with the computers so I'll take a few snaps:
Here's the mat, I think it was cycle ops or something.
Here's the sweat catcher. Same brand maybe?
You can see the evidence of the last ride-off. These tires are miserable anyway, I have a set of DT Swiss wheels with Dura-Ace hubs that I use for the road. I'm a big guy and these wispy little Vuelta rims don't seem like they'll last long. No pot holes on the rollers, though.
This is the gear I ended up in to spin down.