I've been trying to learn about the phrasal verbs. In the beggining I thought that it was an easy matter, but now, I see it as a very extensive problem. There are lots of ways to learn them, but which are the most common phrasal verbs? How can I learn more? What about the separations, particles, etc?
Any dictionary for learners will tell you whether they are separable or not. In our list of them, you will also find that information: http://www.usingenglish.com/reference/phrasal-verbs/
Learn the ones that are relevant to you and your language requirements- note the ones you come across in your reading, conversation, etc, and focus on them.