Visualisations are very powerful thing for understanding algorithms. For the classical CS undergrad ones (DFS, various shortest path or minimal spanning tree ones, and of course all of the sorting), visualisations are easy enough to find on youtube, but with less well known algorithms, sometimes you have to draw one yourself.

Another thing I sometimes do is run a few iterations of the algorithm myself on paper.

Here is a concise PDF of definitions and notation https://docs.google.com/open?id=0B_WU5GXujPOVRDFYRUlKcFF4RWs

It's from CMU's course titled "Concepts of Math" The professor, Brendan Sullivan, just wrote the textbook in an easy to understand style.Here's a link to the course: https://colormygraph.ddt.cs.cmu.edu/21127-f12/ and if you click the AnnotateMyPDF website, you can get a copy of the textbook, practice problems, etc for a more in depth understanding.

You could try Knuth's Art of Computer Programming, Volume 1. It's in a formal style but covers some simpler algorithms and it's by an incredible writer. It's painstaking to read but some find it to be nearly a religious experience.