It is always helpful to search about the person you are about to meet. For a visual artist, whether you follow their work or not, thoroughly search about them and their work. Even a journalist will need to know so much that they can ask questions to the artist. So be prepared about the meeting and have some information before introducing yourself.
At the time of introduction, be realistic. If you do not know any thing about that artist or their work, and happened to just bumped into him, no worries. Just be realistic and ask after casual chit chat start asking questions about their work, and then listen patiently.
If for some reasons you do not hold any information about the famous visual artist you are meeting to, just be realistic and do not throw words around, which even you do not know the meanings of. Talking about things you do not know or have not read about them can make you feel stupid in front of that person.
While introducing yourself to a famous visual artist, maintain a composed posture. Do not shake hands around or shift body weights on your legs. Making some unpleasant gestures can expose in front of the person and you might even become nervous yourself. Just be relaxed shake hand with the artist firmly and let them know who you are and how you feel about meeting them. Be yourself and do not be anxious.
Use of proper words can also help your introduction with the person. Be selective in words and do not use jargon etc. Also maintain a right tone level in your voice. Quality of your voice can tell if you are feeling nervous or just relaxed. Do not talk taller or louder, this can also expose you quicker than you can think of in front of the person.
Listening patiently is also an art of knowing about a person. After formal hello-hi and some introductory remarks, you can let the person speak out and you listen patiently. You can also ask questions in between, but be focused to subject of their interest. This is a good technique, and can help you know what type of the person they are and how much they feel good for talking about their work.