Can student second author go to conference? I am an undergraduate in computer science. 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, he came up with the theory, and I did most of experiment and data analysis and visualization to empirically support it. 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?
As others have already stated, it is perfectly acceptable to show up at a conference when you are not the first author of your paper, or even if you have no paper at all at the conference.

Depending on your research group and how well-funded it is, funding your trip may or may not be a problem. Your first partner in such attempts should certainly be your co-author, and there is nothing wrong about asking him whether you can go and to what extend his grants or the university can support you. The prof. will also know about other funding sources you may apply to. For instance, you could apply as a student volunteer for the conference (usually levies the conference fee), or you could ask for a travel stipend from the conference organizers (although these are often indeed reserved for first authors, at least in my field).

As a sidenote, most professors around me are actually really happy about undergrads that want to go to conferences, as it shows that the undergrad really cares about research and wants to see how it is being done. People love that, because both, in my Swiss current and Austrian previous university, getting good undergrads to stay for a PhD was a perpetual concern and worth quite some money in up-front investment to professors that had some travel money to spare.

(PhD admission works different to the US around here. Most of our PhD students come from our own pool of undergrads, and it's definitely a students market (i.e., few good students, lots of professors looking for them). Good undergrads are basically wooed by professors to do a PhD with them.)