There are various ways to make sure your letters get to your university of choice on time. The first way would be to do it on your own. You would be responsible for giving each professor the envelopes for each recipient graduate school and you would make sure each professor knows the deadlines, etc. This way is doable for several people, but I prefer to use the Letter Service provided by the Career Center.
When you go onto the Career Center website (career.berkeley.edu), there is an option underneath the "Grad/Prof School" tab that states "Letter Service Online." Through this option, you can sign up to be a part of the letter service which will charge you a $20 fee to sign up and will then charge you for each letter afterwards. While this may seem expensive, it guarantees that the graduate schools receive the letters on time and the letter service forms make the entire process seem more organized and professional. Once you have signed up, you must fill out a waiver form for each professor. It is encouraged that you select confidential for your letters. Then you must email this waiver form along with the letter forms given by the service to your professor. Professors normally also want your resume, a rough draft copy of your personal statement, and your unofficial transcript just to have a better idea of what to write so I recommend that you send these as well. Most professors at Berkeley are familiar with this process and are more comfortable using this process rather than your own individualized process. This is a great way to stay organized and on top of your letters of recommendation and you will definitely feel ahead of the game.
About a month before your letters are due, you can send a friendly reminder to your professors about the due date. This process is straightforward and very helpful. Best of luck to you all!