Understand that the Horus Heresy series is not so much a single linear progression, but rather an intertwined set of books covering different events occurring during this era of Warhammer 40K lore.
What I've been doing to get through the series is:
- Check out the core rulebooks and other fluff sources (e.g. Index Astartes entries) for the games. Fluff basically refers to any lore or background information on the game, as opposed to game rules. These sources are great general primers for the 40K universe, the history of the Imperium, and the Horus Heresy. Find topics that may interest you. Examples might include:
- The Great Crusade/years leading up to the Heresy
- The "Shattered Legions" (Space marine legions decimated at the onset of the Heresy)
- Nathaniel Garro
- The Mechanicum
- The Imperium Secundus
- Look up those topics on Lexicanum. This is one of several Warhammer 40K wikis, and the one I find to be the most responsible as far as citing sources. This will give you a general overview of your selected topic, and basically list the books that feature significant events for said topic.
- For example, Lexicanum's entry for the Alpha Legion references Dan Abnett's Legion (Horus Heresy #7), so that's probably a great book to read if you want to learn more about those guys.
2a) Lexicanum is a great source to find new topics of interest as well. Rather than using the rulebooks as a starting point, you may find yourself simply meandering from page to page until you find something really neat and go from there.
- Once you've found a book fitting your topic, give it a read. The basic info you've gathered previously should give you enough to figure out most of what's going on without having to read the entire novel series. If there is anything you're unsure of, head back to Lexicanum to fill in the gaps.
BONUS: While writing this, I came across a neat chart detailing the major story arcs during the series, which map out what novels and short stories to read, and in what order, to follow these arcs. It seems to be up to date as of the release of Master of Mankind in June 2017.
As Shade mentioned in their answer, a more up-to-date and interactive version of this chart is available here, which includes some of the newer series such as the Siege of Terra (outlining the last phase of the Horus Heresy).
Hope this helps. Happy reading!