Can student second author go to conference?

I am an undergraduate in CS. I worked on a professor's project and he submitted it to a conference with me being the second author (he and I are the only authors). If it is accepted, I would really love to attend the conference (I have never done so before), both for knowing what other people are doing and establishing some relation with other professors. However, I am not sure whether it is even appropriate to ask my professor. We are keeping a very friendly relationship and I don't want asking him for this thing to make him perceive me as "conceited" (or something else).

For my contribution to the research, I did most of experiment and data analysis and visualization. It amounts to about 25%-30% of the total length of the paper.

I am completely unclear about funding issue. Do conference organizer provides some compensation? Or should I ask for university for support (I guess they will be at best reluctant since I am not the first author)? Or should I ask for my professor to use his funding? Or do I need to pay my travel expense myself?

Thank you very much.