To explain "read up", I will first explain a more intuitive expression "fill up". When your car is low on gasoline, you drive it into a gas station in order to add gasoline to the tank. You can add just a little bit of gasoline, or a lot, or you can "fill it up". "Filling up" means adding gasoline until the level reaches UP to the top of the tank so that no more gasoline can be added. "Reading up" is a similar expression. Instead of adding gasoline to your car, you are adding knowledge to your brain by reading and reading until your brain is full. Don't interpret that too literally, of course. It is just a metaphor.

Howdy Shana! The phrase “chances are…” has a meaning similar to “it is likely that…”. For a good example, try listening to the old song “Chances Are” by American singer Johnny Mathis. As for “read up”, this is what is known as a “phrasal verb”. Phrasal verbs are usually verbs plus a particle, often collocated with a preposition. Phrasal verbs are tricky because their meaning cannot be intuited just by knowing the definitions of their constituent words, they must be learned one by one. I recommend the book Phrasal Verbs in Use for getting familiar with this subject. Give me a holler if you have any questions!

Read up has more of a sense of learning and understanding rather than simply reading about, which might be more for general interest.

"reading up on" just means "reading about". The first way is a bit more casual / informal.