To start with the timing: don't mention everyone in the beginning. Most readers will not be able to memorize all of them anyway, so you might as well use the reader's short attention span to your benefit. Start with the characters that really matter, and make sure to introduce them in a way that makes us remember them. How, then, do you do that?
Simple ways of creating unique characters
It's a good idea to give all your characters specific traits, so that the readers will not get them mixed up. One of the most obvious ways of doing this is to allot them different genders. This isn't possible or necessary in all books (Tolkien certainly made no attempt at balancing the number of male and female characters, for instance, though certain *cough*me*cough* females might also suggest that this is part of what makes his books somewhat
Physical appearance is another way of making your characters recognizable. Who would remember Quasimodo without his hunchback? Would Long John Silver be as scary without his wooden leg? Anne of Green Gables would not be the same had she not had vivid red hair.
Finally, a frequently used trick is creative naming of characters. Naming can be difficult (says the woman who accidentally called three characters within the same story Fred…). One of the big things to avoid is several characters with names that sound similar. Try not to give all of them short, common names; but don't give all of them long, elaborate ones either (I am looking at you, Dostoyevsky….). Also, it is wise not to use too many names with the same first character (unless there is a point to it). Archie, Bree and Carla are much easier to keep apart than Archie, Arnie and Arnold.
Slightly more complicated ways of making your characters unique
All characters have a back story, even if these aren't always necessary to put in the actual book. Use what you know of their back stories to consider what roles they play. A character may be the hero of the story, but she can also be a wife, a mother, a daughter, a boss, and so on. Her family relations, other relationships, vocation, nationality, moods or interests might be what make her unique and memorable to the reader. And keep in mind that these things don't have to be stereotypes (even if they often are). I tend to find it easier (and funnier) with characters that have original and specific roles that make them very easy to distinguish. JK Rowling did a spectacular job with this, especially on the character Albus Dumbledore. Although he featured in the very first chapter of the first Harry Potter book, his real introduction came a few chapters later, on a chocolate frog card:
Dumbledore is particularly famous for his defeat of the dark wizard Grindelwald in 1945, for the discovery of the twelve uses of dragon's blood, and his work on alchemy with his partner, Nicolas Flamel. Professor Dumbledore enjoys chamber music and tenpin bowling.The information might seem random, but in reality several of these facts had a huge impact on the plot of the books.
Further, make sure that all of your characters have a purpose, or a function in the story. Character functions are very notable in fairy tales. You have a hero; a villain; a giver (the person who gives the hero one or more necessary item[s]); a helper (sometimes this is the same as the giver); a sender (the one who sends the hero on his mission); a false hero (this would be the role played by Cinderella's stepsisters, who try on her shoe and fails); and finally the character[s] called "the Princess and her Father", which basically translates to whomever is being helped or rescued by the hero.
All of these characters have very specific functions in fairytales, but often this list can be recognized in other stories as well. Take Agatha Christie’s books. Poirot is the hero. The murderer is the villain. The sender is the person who requested Poirot’s assistance. The helper is Hastings. The giver can be anyone who provides clues that eventually help Poirot solve the case. Finally, there always is a princess and a father in Agatha Christie’s books (even if one or both of them may turn out to be the false hero).
Even if you do manage to create unique characters by use of the above tips or otherwise, it remains a challenge to introduce all these things to the reader without making it seem like unnecessary page fill. Since we cannot all invent chocolate frog cards, the trick is to find a way of weaving in the necessary information without cluttering the story. My best tip here is that actions and speech may give away more about a character than descriptions. "He was curious about the content of the boxes" is much less intriguing than "His eyes darted back and forth between the boxes, his voice almost ecstatic when he finally asked: 'What's in them?'" (Which incidentally is an example of "show, not tell" – heard that one before much?)
Fix it in the edits
If you get the feeling that your story is getting bogged down by too many characters, it might be an idea to do something about it at the editing stage. Try to sort out any characters that serve only one purpose in the story. Did you know that Shakespeare originally wrote the character Friar Laurence as two characters? One who was a vicar, and then one who was a chemist. Shakespeare needed a clergyman because someone had to marry the young couple. He needed a chemist, well – you all know the story. Chemist Laurence wasn't cooking meth. Anyway, once Shakespeare had finished the play he realized that he had a lot of characters, and that would require hiring a lot of actors, which was very expensive. Thus he got the brilliant idea of merging two of his characters, the vicar and the chemist, into a single peace-loving, chemistry-savvy friar. (And no, you cannot quote this if you are writing a ground-breaking PhD about Shakespeare, since I naturally made the above up.)
Finally, if your last name starts with a D and ends with ostoyevsky (which is just one of the many transliterations that will make you eligible for this last piece of advice), and you absolutely insist on keeping all of your 140 characters with impossible-to-remember names, I highly recommend adding a "List of Cast" (or dramatis personae as it was originally suggested in our discussion by… No, I'll let that particular dragon-loving viola player remain anonymous) at the very beginning of your book. At least the reader will know where to go back to…