Read the epics twice
First a "fast read" to catch the storyline and get familiar with the names; then a "close read," line by line, to taste the real flavor. Lay a foundation with this site’s figure cards and timeline first, and the original text will go down much easier.
Learn about Greek theater before reading the tragedies
Look up what an ancient Greek theater looked like, the masks the actors wore, and how many actors each playwright typically used — with that background you can "see" the stage far more easily as you read.
Read several versions of the same myth
Reading them side by side shows which details are the shared core across all versions and which are one author’s personal invention. This site flags "version differences" on a few key figure cards as a demonstration of exactly this.