Everyone has very good suggestions here and I think you should base it off of the person you're asking. If you think they would prefer an in person meeting then definitely find a way to get to their office.
Personally I emailed all my writers first and said I was interested in them writing a letter for me, but understood that with so many students it isn't easy to get to know me through lectures. I then asked if I could schedule a meeting with them to talk to them about myself, my qualities, my desire to be a physician, and why I think I will make a good physician. Pretty much I just made a very strong argument for myself in hopes that they would see that and learn a bit more about me so they are more comfortable writing me a letter.
I also put together a personal folder with many things about me. I highly highly highly highly highly recommend this because they may not actually sit down to write the letter until later and they may have forgotten some things. In my folder I included copies of my resume, transcript, a bullet point list about my qualities that was a summary of my presentation to them, and copies of many of my awards I have received over the years (I am a Marine veteran and had some personal decorations throughout my time in the Marine Corps). Everyone really liked that I was extremely organized, thorough, and thoughtful into this process, because with the sheer number of students these professors have asking them for letters, it can get a little hectic for them. They may only want to write letters to those who are organized and make a good argument for them self.
Finding letter writers is extremely stressful (or at least I found it to be) so get started early on in the process and don't wait until the last minute to do it. Hope my suggestions work!