It seems to me that I read someplace (maybe at your blog?) that you've written for the Friend for many years. Is that correct? If so, I'm wondering ... were you employed by them as staff, or are you talking as a freelance writer?
I've submitted several times to them and never seem to get anywhere. Have you got any suggestions? There must be some trick I'm missing!:-)
Yes, I've written for "The Friend" for many years, and no, I was not on the staff. I worked purely as a freelance writer. As far as tips go, I think subject matter--as long as you write it decently enough--is one of the most important things to consider. For instance, I always think about what message I am giving the readers, who are, by the way, children, parents, and church (especially Primary) leaders/teachers. I also make sure that what I am "teaching," without being didactic, is exactly consistent with church policy.
Similarly, I not only narrow the focus of my message, but I also make it unique. That means, rather than simply relating a story that teaches "God answers prayers," I look for another, less covered topic that is also part of the same story. An example of this is my story, "The Walking Bible." In it, a missionary receives an answer to his prayers, but he also faces and overcomes the disabling effects of illiteracy.
Another thing I've done (more in the early years than now) is "study" the magazine--everything from what kinds of stories, articles, activities they are publishing to "how" they are written. One way to do this is to take apart, i.e., outline, them to get a feel for their structure. THAT really helped me get into other mags, too.
Finally, keep an eye, an ear, and your creative teaching mind open for good stories and good ideas for puzzles, etc. (if that's what you're interested in). Kids love them and teachers need them.
BTW, I believe they are only accepting non-fiction right now. It might also help you to know that their publishing schedule is at least one year in advance. For more information, see their guidelines at LDS.org.
Hope this helps.