Its’ not so difficult, believe me!
The trick is to make it easy, both for them and for you, to visually check whether each student has participated or not. I use a very simple method: paper cards that are green on one side, and red on the other. Every time a student asks a question or adds a (somewhat substantial) comment, they get to turn their card from red to green.
It’s all explained in this little video:
By the end of class, you can see with just a glimpse which students still have red cards on their desks. If you have a “participation grade”, it will take you no more than a minute to pen down which students got their points, and which didn’t. (That is, when you’ve learned all their names. At the beginning of a course it may take a bit longer.)
The neat thing is that students immediately know whether they are getting their points or not, and will make an extra effort – I normally get about 80% of the students to participate in one form or another without prompting. Which makes it also easier to pay attention to the students that find it more difficult to participate, and to help them out.
This system also helps you to avoid a student “hogging” the discussion without being curt to them: if a student is raising their hand for the tenth time (it’s a good problem; I love those students!) you can simply say, “Let’s hear from the red cards first.” A very easy way to open the discussion.
Let me know if this was any help!