Hi :) I started my daughter on time-outs at the age of 20 months, so you're in good company :) I will post my step-by-step below.
You really do have to isolate them from any and all distractions. I've found this to be extremely important. Also, when one child is in time out, I make sure to keep the other out of eyesight and play with them to keep them from wandering into the discipline area. I also ask them to be quiet, but that's really a shot in the dark. It's only a minute and a half, so it's not a big deal to break from whatever we're doing.
I have a chair that we use at the dinner table. It's too big for her to get out of, and she's very good about not "falling" out of the chair or trying to get out of it.
I put the chair in the corner, by her bedroom door (which is at the end of a very short hallway). I close her bedroom door and put her in the hallway, facing her door, in the corner that doesn't have the door knob (so she can't play with it). I make sure to never be severe and to be very calm when I put her down in the chair. I tell her, "Because you ____, you have to go to time out." Then I walk away calmly. Short and simple for their burgeoning language skills. I usually put her in for a minute and a half, sometimes 2 since she's getting closer to 24 months.
When she is done, I go to her (leaving her in the chair), get on my knees, eye to eye with her, and ask, "Do you know why Mommy put you in Time Out? It's because you ________. No ____________. If you __________ than Mommy has to put you in Time Out. Alright? Can you say Sorry? (she says "awwy") I say, "Good girl! All done!" Then I take her out of her chair, give her a hug, tell her she's a good girl, tell her not to do the behavior, and then say, "I love you! Go play and have fun!"
It must work, because she no longer screams when she's upset about something, and when she does scream, I just say, "Do you want to go to Time Out? Cuz when you scream when you're angry, you're telling Mommy you want to go to Time Out" and she stops immediately (at this point, I usually ask her what's wrong and encourage her to "use her words" and "tell Mommy" which works surprisingly well for her). She also used to run away from me if I asked her to give me something she couldn't play with (like my cell phone). But now, if I ask her politely to give it back, she does it about 95% of the time. Woohoo!
I have also found that it is EXTREMELY important to be very very calm when I discipline her (or at least it is this way with my child). Before, when I would try to discipline her, it never seemed to work. I realized I was shooting myself in the foot by getting upset and talking to her in a severe voice. Kids really do regurgitate their parents' behavior. So now, I NEVER use a severe voice or just say "NO!" with her unless she's poking her eye with her dinner fork or something hazardous like that. I always ASK her to do things with a pleasant voice instead of ordering her with an authoritarian voice. When I take her to Time Out, I do it calmly, I talk calmly, I make sure that she doesn't see or feel anger from me. I am amazed at the difference it has made not only in disciplining her, but in her overall behavior. She is a much happier, much calmer child.
Hope this all works! Good luck!