When I first started Jiu-Jitsu, I wished I had a list of general theories on grappling, simple tips that would be easy for me to understand and remember. Now that I've gained a little knowledge, I've decided to create my own list, for any beginners who might want one. These are just some basic things that I've learned as a six-month blue belt, that I hope might be helpful to others.
1. Keep your limbs bent. There are exceptions to this (ie. when you're sprawling), but generally you do not want to straighten and extend your arms and legs. Bent limbs are stronger. Are your arms straight when you pick up heavy things? Not unless you are Frankenstein.
2. Don't let your arms cross the center line. Again, there are exceptions (ie. gi chokes), but mainly you should keep your arms on their respective sides. Not doing so could easily set you up for an armbar or reversal. Pretend that your arms are mortal enemies, and keep them separated.
3. When you are on top of your opponent, try to keep your weight spread out on them diagonally. If you are too far on one side, or too high or low, you probably won't be on top for long.
4. Use your entire body weight. This goes for pinning, submissions and escapes. For example, trying to kimura someone with only your arms relies too much on muscle. You need to position yourself so that you can put your body weight into play. When trying to escape from things like a triangle or straight armbar, stacking your opponent up and dropping your weight on them is a lot more effective than just trying to pull out of it.
5. Underhooks, underhooks, underhooks. Holding onto the head is fine in some cases, but usually if you really want to control your opponent, you should be thinking about underhooking an arm. Repeat after me: "I will stop hugging heads, and start hugging arms."
6. When you are on the bottom, don't remain flat on your back. Try to get turned to the side, which will alleviate a great deal of the pressure on your chest. Unless you like being crushed and not being able to breathe, then just keep laying there.
7. Along with trying to get to your side, if someone is on top of you, don't underestimate the power of framing. You need to get your arms between you and your opponent to create space. Escapes can't happen if there's no room to move.
8. Don't turn your back to your opponent. There are some advanced techniques in which you do so, but beginners should never turn away from someone. You are just asking for them to take your back. Sometimes upper belts will even try to bait you by giving you an opening in which turning away seems like a good idea. Don't fall for it, they are evil and will laugh at you if you do.
9. Protect ya neck. If someone starts circling, immediately block their attempt by tucking your chin and framing with your arms (as if you are talking on the phone). Never let anyone grab the collar of your gi. Especially not me.
10. Don't forget to breathe. That might seem stupid, but hey, I still do it all the time.