Angel,
Definitely don't worry about the time it's going to take you (or about the time you have spent thus far) to learn all of these techniques. I still don't get it all right, especially when I'm depressed (like today). 
I find it really hard to do anything when I'm feeling this way, but because I learned some CBT there's now a little voice in my head saying "Okay, today's a bad day, so what can I do to help myself? What is manageable for me today?" And on days like this, if I am stressed, if there are things that are upsetting me or on my mind, then I am going to try to sort through them--so that I can bring some relief to my symptoms. I can do that by those thought diary exercises, or by writing in my journal or talking to a friend. I make sure that I try to change the negative thinking; recognize that the depression is making me feel certain things.
But like I said before, sometimes this isn't all possible during deep depression. That's when I need to accept that and do things to just take care of myself.
CBT of course comes in many forms. There are exercises, and then there are more subtle things, like what I mentioned in the first paragraph. For me CBT means "doing" something to help yourself; "doing" something to fight the illness, even if it's just a little something. Just something that is manageable, because it's important not over-do things. Before I learned CBT, days like today would be scary for me. But now all day, even though I am not well, I'm going to be trying to get myself through the day.
To remember the distortions--it's going to take time b/c our memories I think are a bit challenged with meds/depression...Just refer to the definitions you were given...I always have to have that list in front of me to know which ones are which.
The situations--I'm not quite sure how your therapist is having you do this exercise, but when I learned it, mostly the situation was something that was a stressor (I find that is usually pretty easy to identify)or something that I am thinking negatively about, a lot. I'll give you an example of a negative thought/feeling I was experiencing...Before I left my job, I was having a hard time with my manager. She made me feel like I wasn't good enough, that she didn't like me. It made me feel really bad about myself (that was the situation) But the fact, the truth, was that I was one of the hardest working people there. I followed all the rules, never did anything wrong. I didn't miss work and I also went above and beyond, doing things outside my job description. I was an excellent employee. Once I wrote all of that, I would read it over before work and eventually I was mostly thinking about how wrong she was, and how proud of myself I needed to be, everyday. Before I did that all I could feel everyday was how bad she was making me feel....
Anyway, sorry for long post, hope that helped a little. You have tons of time, you can do it!