My daughter was around 2-years-old when we began the weaning process. We started with removing it from naptime and only allowing it at bedtime. For the first few days, she was not to happy with this, but 3 or 4 days into it the screaming stopped and she was sleeping just fine (probably from the exhaustion of screaming - lol!!!)
We created her a Countdown Chart that showed her how many days she had left with her suckie . . . example: The chart had 7 boxes on it which indicated that she had 7 days until she got to say Good-Bye to her suckie. Each morning when she woke up, she put a sticker on her chart. We talked about how many days she had left and made sure she understood that when the chart is full, she was all done!
When her chart was full, we made a really big deal about how big she was and how big girls don't need suckies anymore! We had arranged for the last day with the suckie to also be on garbage day. That morning, we all walked out to the garbage can and let her throw it away. Then when the garbage truck came, we all stood at the window and waved good-bye to the suckie!!! I then let her call a few people (grandparents, aunt, etc) to tell them what she had just done!
Then later that night, we celebrated with cake, ice cream, and party hats!!! She felt so proud that by bedtime, she was totally ok with going to bed "like a big girl"! For the first few days without it, she asked about her suckie but we very excitedly reminded her that she threw it away and the garbage truck took it away!!!
I am happy to say that she never had a problem without it!!! Good luck!!