I may not be as fast as some people here, but I do average low 9. I remember being at around 11 seconds for a little while, and this is what helped massively for me:
1: Untimed solves. Focus on doing untimed solves where you have fluid, pause-less F2L, or at least mostly pause-less. Don’t try to turn at your normal speed, go as slow or as fast as you need to. Say you start out and can only do 1 TPS in order to have fluid F2L. Once you see that F2L at that speed isn’t challenging anymore, up the speed to 2 TPS, etc. Basically, you want to try to have smooth F2L, but also that you go at a speed that is slightly challenging for you.
2: 2-Gen solves: 2-Gen helped me a lot, mostly for TPS increase, but also for lookahead. 2-Gen is also a fun thing to practice.
3: Do deliberate practice: You need deliberate practice, aka, don’t just do solves, rather, pinpoint your weaknesses and deliberately improve on them. For example, if you notice your cross could use some work, then do some untimed solves where you try to improve your cross solutions. If you notice some of your algs are slow, drill them to at least get them reasonably fast. I remember loving the Ra Perm, but being slow at it compared to other of my PLLs, so I drilled it for a few days and it massively improved.
4: Casual solves: Another thing that can help, although I didn’t do too much of, is causal solves. This just means taking your 3x3, or whatever cube, and just do some random solves on it. Not timed, just for fun. I found this helped me find new F2L solutions I hadn’t been able to spot before when I speedsolved.
5: You can try doing causal/untimed solves where you try to insert the first 2 F2L pairs in the back, always. You’ll see how much easier F2L is after that, and it is a good habit to insert pairs into the back first. (Unless of course you have a really easy first/second pair that goes in the front slots).
6: Timed F2L: I started doing this maybe when I averaged high 10, but it also has helped. Start a CsTimer session where you have cross solved, and then time just your F2L. This is a fun exercise for me and helps your lookahead in the long run. It’s also great to do this if your F2L lookahead is suffering on some days, and can help you diagnose if your lookahead/F2L solutions need more work.
8: If you have a 4x4 or bigger, do loads of wolves on those. Not only it helps you improve your 4x4 (or whatever cube you have) times, but it helps with lookahead on 3x3.
7: You’ll notice most/all of these ”tips” are lookahead/F2L based. That’s because it is the most crucial part. I see people who learn many algs thinking it makes them faster, which they do for a little while, but they don’t work on their F2L efficiency and lookahead. If you can get good at lookahead, your averages will drop significantly.
8: Don’t give up! Some of these tips, like 2-Gen, may seem like they do nothing in the first few days/weeks. But trust me, they will help you out big-time in the long run. Edited to add: Of course, do all this but still do times solves! I’m not saying to completely avoid timed solves at all.
9: Bonus: I know I’ve been through these, and they are terrible. I’m talking about slumps, especially big ones. I remember averaging mid-10 and going through a 3 week or so slump of averaging 13 sec or something like that. It was annoying and frustrating that I couldn’t get my normal times for whatever reason. My solution to these slumps is… do all of the above tips. If you notice you’ve been in a slump for a while, try to see why. For me, it usually was lookahead just not being as good as it can be, so in the time I was in a slump, I did all of the tips above and ignored normal timed solves for the most part. Eventually you’ll get out of the slump, and, if you practice on your weaknesses meanwhile, you’ll come out of the slump better than ever before.
10: 2nd Bonus: I like warming up before a 3x3 session with drilling algs or learning new ones. I’m trying to finish full OLL, and so what I do before a session, is do a 30-50 OLL drill sessions, or learn a new OLL, along with drilling. Not only is it kind of fun, and it helps you improve your algs, but you also get nice and warmed up and ready for a great session. It’s a triple win!