I wwould go to them during their office hours and ask in person. If they say yes, you can say you will follow up with an e-mail giving them the specifics.

I’d suggest asking them in person, and saying something like, “I really liked having you as a teacher, and loved your class, would you mind possibly writing me a recommendation?”

Or something of that sort.

You should only ask professors who know who you are.

I would ask them in person, not over email. They have most likely had to do this in the past many times, and it shouldn’t be a big deal for them to do it again. Just tell them about the graduate position you are applying for, and ask politely.

If you have one or two professors that you have befriended, or professors that taught smaller classes, ask them as opposed to professors who may not know you as well.

I would contact them over email to schedule a time to grab coffee and/or chat in their office. However, I have asked over email and in person depending on surrounding circumstances (distance, availability, deadline).

I’m in the process of applying to transfer out of my current program, and this is how I’ve formatted my in-person request conversations:
“I am in the process of applying to X Grad School because of ABC. I wanted to know if you would feel comfortable writing a letter of recommendation for me. The deadline is Y.”

Ohh I guess I should tell you that my department is very small (only 5 professors and no more than 25 students) and we are like a little family. I have all of their cell and home phones and they have mine, we all have been out for drinks and food a couple times. We’re not best friends or anything but they do know me and like me.

Be as specific as you can about what you will need the recommendation to look like. One school that I applied to required that all of the letters of recommendation be on THEIR paper. Make sure that you have all of that stuff on hand so that you can give it to them if they agree to write the letter. If the deadline is more than a week or two away, it might not hurt to check in with them as the deadline approaches to make sure that your letter didn’t get misplaced or overlooked.

@nayeight That was how my undergrad experience was, and I’ve had close relationships with professors at my current institution as well. Knowing that, I’d recommend even more just shooting them an email asking when they’re free to get together for half hour or so. It’s also a great opportunity to get a little feedback and advice from someone who has obviously gone through the process before. My situation is a little weird since I’m having to explain to my current professors why I don’t want to stay (administrative and overall fit), but I was still able to articulate to them why I wanted to do this, which is then information they can incorporate into the letter.

I agree with @torch81, tell them the process and help them in any way you can. Offer resumes, transcripts, statement of intents, if they want them, and remind them of what might have made you memorable in a class.

Given the nature of your department, you definitely have to ask in person. Email and ask when they have time to talk (“Dear Prof So-and-So, Hope all is well with you. I’d like to meet with you in the next week or so, what time is good for you? Thanks! nayeight”)

And then ask. Come prepared with all necessary documents. Be ready to talk about what you want to go to graduate school for and why.

GOOD LUCK!