How do you view the blogs you follow?

I need your help? I want to know what is the best way to view the blogs that you read. 

I usually use Blogger. It gives me a feed of all the blogs I 'follow' and shows me posts from most recent. I really like how it shows it, it gives me a little picture and then shows me the first few lines of the post, so I can see if its something I am interested in reading. 

But lately I have been having some problems with it. Some of the blogs I follow don't show up in my feed at all. For a while I just thought those people hadn't posted in a while, but when I went to their actual blog, I missed like 20 or so posts, but blogger is still showing I follow it. My feed also sometimes shows blogs that I don't follow anymore, which is annoying to sift through all of those. 

Another problem I have is sometimes I find a blog I like (Pioneer Woman, Tip Junkie, etc.) that do not have an option to 'follow' them in blogger. And so I never ever view their blogs because I forget to look at them since its not on my feed. But I would love to follow them. 

So what are my other options? I have seen that you can follow blogs by email, but I really don't want to do that, I know I would never read any of that stuff, I would get so many emails a day too, that it would drive me crazy. I also follow blogs on facebook, but facebook is changing its ways and I know that you don't see all of the person's posts if they are a business like some blogs. What is RSS feed? I have heard of it, but not quite sure. 

I am asking this question so I can follow and view more blogs, and also so I can update this blog a little better and be more convenient for my readers. 

PLEASE let me know what you do in the comments. I appreciate it so much!