I'll be at a conference next month to present my paper. I have a Master's degree in Computer Science and now I'm looking for a PhD with scholarship. Well, is it right, with a common sense and in a polite way, to ask a professor at conference about a PhD position?
I think it is OK but, before you attend that conference; try to identify the professors who come to the discussion panels and sessions. Their names are normally written in the conferences' websites. Then search their university homepage on the net and read some of their publications. This way you find two or three professors that their research interest is almost near yours. At the day of the conference, go to the sessions in which they present and politely after a short introduction about yourself; ask whether they accept any PhD student or plan to accept one or not.
I have seen that some MSc students go to the conferences and ask any professor they see without any previous search about their academic background. This behavior is so impolite.
Sometimes, in the professors' website, they have notifications about not accepting new PhD students. In this case, asking them for a PhD position is not acceptable and means that the person has never visited his website and probably he is not a good student at all. This way, they may not even listen what you are talking to about.
If in some cases, there are some positions available and notified on their website, then go to that professor, show them your curriculum vitae and ask them for a position; or talk to them about opportunities available for a PhD student.
If you are interested in working with a professor but there are not any positions available; then talk about doing some volunteer research under their supervision. However, it all depends on your research background and how much they find you suitable for working on a research topic. For instance, if you have a good programming background and they need a programmer in their research group, they may accept you to work on some parts of their research project; and after a few months, if any PhD position become available, you will have a higher chance to compete for that position, because the professor knows you better as you have previously worked with him.
Conferences are so valuable for the research students to become familiar with ongoing research projects and publications. In these conferences, you may talk to other researchers or PhD students and start a research project which is interesting for both of you. So, do not miss the chance to discuss and talk to the other people at the conference; and not just focus on the professors. Besides to these, some companies may need a person like you who has done a research in the field of your interest. So talk to them. There may be some funding or grants available which you can apply for.
I think that if you have your paper printed with your resume attached to it may help the professor to remember you and if any positions be available in future, he may contact you. Remember that not all the people have good memory to remember the others with detailed information about their resume and paper. People easily forget details about the past. If your resume be interesting for them and they forget you because they have no printed information about you, then you may miss a research position.
It is definitely OK. You should be more like @JeffE suggests "How do I apply?" rather than "Would you accept me for a PhD?".
Conference is a great opportunity to meet and discuss with your potential supervisor. You should try to judge, as much as possible, how easy would it be to work with that person for quite a few years. On the other hand, note that high profile academics are used to get approached by random people and you shouldn't be discouraged to formally apply even if they seem way too busy to have a long chat with you.