Many of the journals listed here allow free access to their issues, while others require a subscription fee. Either way, this listing puts together a variety of peer reviewed journals from many different subject areas, many of which will be of interest to teachers.
The National Science Foundation has created a position paper on the use of research in guiding teaching practice. While this is very superficial in that it does not offer any specific ideas about how to incorporate research, the fact that a major government agency has a position on the subject is quite remarkable.
There is no shortage of peer-reviewed education journals. As seen in this listing, there are hundreds from which to choose. Many of these have links to the journal's website. This is a wonderful collection!
The American Educational Research Association is a leader in high quality, scientific, peer-reviewed education journals. Many of them are available online (some require membership in the organization). These journals are excellent sources of information and cover a wide breath of topics.
What is the connection between research and teaching? It is only through research that teachers can find out the best practices of what works in the classroom. I like this video and think that it works well to outline the basic ideas of research and teaching.
This short video provides some good advice as to why teachers should incorporate research into their teaching. It would be best viewed when just starting out, as the points it makes are quite rudimentary, but useful.
ERIC is an enormous clearinghouse for educational research. Every topic imaginable can be found in their huge database. Most of the articles are peer-reviewed, but there are some that have not been. I suggest using ERIC as a first place to start when researching any educational topic. Chances are you will find it here.