How can an undergraduate be recognized for work done on a paper, with a fellow PhD student and a professor?
The best thing you can do to ensure your work is recognized and credited is to have honest, open communications with the other people you’re working with. So long as everybody’s clear on who is doing what, and everybody is acting ethically, you shouldn’t run into problems.
However, my university has no official undergraduate research program, so everything (i.e. any research conducted) will likely be done on an informal basis.
Except for very large projects, essentially all research collaboration is done "on an informal basis". You've seen that being on a formal undergraduate research programme and being a PhD student both give some sort of formal basis to a research collaboration and you've incorrectly generalized. For example, if two professors in your department are chatting over coffee and decide to collaborate on something, there is no formal programme that either one is a part of.
Authorship of research papers isn't decided by looking at the staff list of some formal collaboration: it is decided who contributed intellectually to the work. If you, the PhD student and the professor work together on something and that work leads to a paper, you should all be co-authors of that paper. The reason that PhD students' advisors are very often co-authors of papers is that the advisor very often contributes intellectually to their student's work, and not because of the existence of the formal student–advisor relationship.
My main question is this, how can I protect the work that I do on a project like this? What measures can I take to ensure that whatever work I do is credited, if the paper containing my work is published?
In the normal run of events, you shouldn't need to protect anything or do anything to ensure you receive credit (i.e., co-authorship).
What measures can I take to ensure that whatever work I do is credited, if the paper containing my work is published?
Unlike other answers, I'll mention that it is not unheard of for higher-ups to fail to credit more junior collaborators. So while you have no reason to believe this will happen in your case, some relatively-benign protective measure may be in order.
I would suggest one (or more) of the following:
- Using some relevant on-line collaboration tool - such as a git/mercurial repository for paper drafts, or a Dropbox/Box.com/OwnCloud shared folder through which you exchange files - preferably one which they cannot delete on their own.
- A bit of "wordsmithing" in some of your email exchanges with them so that whoever reads the email exchange understands that either some of the work is assigned to you, or some of the results were obtained by you. Things like doing a bit of planning or roadmapping over email typically achieve this effect without sounding off.
- Engineering one or more occasions in which you and one of the other two are discussing your joint work in the presence of a third party with closer/better relations to you than to them.
The first two you could probably do regardless of wanting to protect yourself; the third one involves at most a bit of bragging, which is understandable for an undergrad and can be minimized.
Each of these reduces the degree of plausible deniability in a theoretical argument about credit, and even more importantly, discourages the very inclination your senior collaborators may have to ignore your contribution.
A side-note: There could be three scenarios here regarding the extent of your contribution to such work.
- Sufficient to merit co-authorship
- Sufficient to merit a "crediting mention" ("The authors wish to thank Ms. Jane Smith for useful comments regarding frobnicating the bar").
- Less sufficient
... and with you being an undergrad it will be hard for you to tell the difference between these three. So if you feel you're being under-credited, consult other people first, discretely, for their opinion on this.
Good luck and I hope you don't need any of this advice!