Learn general chess theory and play longer games. I would recommend only lightly going over common openings, or ignoring them altogether. No matter how complex a position is, chess principles will still apply and it would be a good idea to get these down to an art form.
From beginner to intermediate... how?

Strong fundamentals will take you far. Forget opening theory by the way. That's literally the last thing you need.
Play play play play lots of games. Also do lots of tactics. Not timed tactics, try to solve it all the way before making your first move (if doing tactics online).
IMO that should be 90% or more of your diet right now. Other 10% lets say is opening principals and basic mates.
What playing and tactics do for you is building strong fundamental skills. For example noticing threats, calculation, visualization, and tactical themes.

Avoid blitz and invest in slower (atleast 30 minutes) games with slightly stronger opposition. Create a feedback loop where you get this game critiqued by stronger players who will tell you to both
i) "DO" stuff different and "
ii) NOT DO stuff that you are doing".
Absorb this information + strive to not make the SAME mistakes in your next game. Rinse and repeat :)
The above improvement loop is the sole reason motivated + type "A" players who regularly just go to local chess clubs and couldn't give a damn about studying or structured practice just get better ... really, really quickly.
Disclaimer: Once you become reasonably decent as a club player, you would eventually want to start studying up a bit! :)
I agree with slower time controls. blitz usually reinforces the bad habits than good and with little time to think you aren't going to make many new good habits compared to making bad one's. 30+ minutes per game should be the minimum. I really like the 3day/move here because you can have plenty of time analyzing the different positions and trying to find the best moves that you can and learning a lot in the process. If I was in your position, which isn't far off from where I am, I would focus on playing a handful of 3day/move games, maybe 4 or so, and try to play one Live game every other day with a time control of 30+minutes or greater. After every game that you finish go over it by yourself and look for any mistakes that you can see that you made. Write notes if possible, and maybe any thoughts you remember during the game, moves you looked at and so on. Then post your games here on chess.com with all those notes and get feedback from stronger players. While doing all that find a place to solve chess puzzles, here, chesstempo, a book of puzzles, whatever suits you, and work with five or more a day. Make sure you understand them all, those you couldn't solve find the solution in the back of the book or if online click through the solution a few times and understand why you couldn't solve it. I also recommend finding games from masters, especially annotated games, and reviewing how the masters play and learning how they chose moves and why.
I think chess is similar to learning to write good essays, it isn't necessarily good to do a huge volume of essays to improve at writing them, but looking at known good ones, slowly writing one at a time, reviewing it, getting feedback from others that are good at it, and learning more about the fundamentals of language and writing. My opinion anyway. :)
I started playing chess two months ago and have fallen in love with the complexity of the game. I improved my rating from the 500s to about 750 recently (I know, I know- still extremely low) on ten-minute blitz games and am trying to break 800... What are the best methods to improve my score to about 1200 or 1300? Play, play, play; or learn opening theory, perhaps?