Some of you may know that recently I've changed jobs just prior to Christmas from working as a Graphic Designer to now being a Fund-raising Officer. I see a huge question mark above your head wondering 'how?' and 'why' right now, and the quick reply is I originally come from an events management background.
One thing I've come across throughout my various jobs is that people are to scared to ask, if you don't ask you don't know. Though in saying that do be prepared.
In the case of an artist there is no point going to a gallery and telling them about what you do unless you have pictures on hand. Your better of taking a card and sending an email when you do or if you can go back when you've something to show them.
Same with asking for sponsorship for an exhibition, have as much information as possible, they want to see pictures and really get a feel for what the exhibition is about.
Be prepared to be asked questions. Yes, I've had those stumbling moments. Tell them your thinking about it and when you've an answer you'll let them know.
At the end of the day if you don't ask you don't know and be prepared to accept 'no' as an answer. In saying that the people who have been very rude in their rejections when I've been calling them about goods for an auction, they've lost a potential customer. On the other hand if you do get asked and need to say no, do so in polite manner, as you may get a sale or two out of it.