Research Experience for Undergrads (REU)

This National Science Foundation program is designed to give undergraduates, especially those from smaller schools, a chance to gain real research experience for a summer. Personally I participated in one official REU and one program modeling on REUs. I learned a lot (and they were tons of fun!). The best part is not the specific topic you research, but the opportunity to learn how to be a researcher.
Most of the applications are due in February. Check out the the official NSF REU website for the latest details.
When you are ready to apply, go here to search for programs of REUs in various subjects. Also, search the internet for other research opportunities; Harvard has a nice list of research programs for undergrads. For more detailed tips on applications, I recommend this site
If you want to get an idea of what an REU is like, here are some interviews of past Math REU participants. And also keep in mind these research tips for undergrads if you do get an REU.

QFT Resources

Quantum Field Theory is a notoriously difficult subject to learn, but I found the following resources to be extremely helpful when I took the course a few years ago. I just learned about a few resources that I wish I had then, so here are my current tips for learning QFT. 
Tony Zee’s book QFT in a Nutshell provides a great intuition into what QFT is all about. If you actually want to do calculations, then Peskin and Schroeder’s book is a nice compliment. These two books were the heart of my studies into QFT.
David Tong’s Notes:
Great set of lecture notes that provides a different perspective.
Sidney Coleman’s Lectures:
Apparently, all modern QFT books are based on Coleman (since all the authors learned QFT from him or his students), and you can still see the original videos.  For years there was a set of hand-written notes that served as a transcript of the video but this was recently LaTeXed and shared on the ArXiv.