The two options are wing it until you find some sort of research, and then figure out that research by guessing at it (I've heard claims that the description of the research can assist you with this, but from what I've seen the descriptions are not very informative), or you can look up a cheat sheet/tutorial on ThaumCraft3 and find all of the steps for researching there.
You can switch between the two options as needed, of course. For example, you are stuck researching something that you're pretty sure you've tried everything to find. Instead of giving up like when you're stuck on an Angry Birds level, or the like, you can just hop online and find out what you are missing.
Good luck!