Can student second author go to conference?
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.)