Andrew Smith is a 3rd-degree BJJ black belt based out of Richmond, VA (Revolution BJJ). He runs BJJ Path, a video tutorial website.
Pulling Guard, the Necessary Evil
Pulling guard in sport Brazilian Jiu Jitsu might be considered a necessary evil, but it's also an incredibly practical one to understand, whether you determine you're overmatched on the feet and are about to be taken down, compete better from your guard, or want to understand from the other point of view so that you can prevent the guard pull from happening in the first place. Note: we are not going to cover how to jump guard, because I've seen more serious injuries from jumping guard in sport BJJ competitions than any individual submission, and people often dramatically underestimate how unsafe the process is. Instead, we'll look at how to get both parties to the ground safely here, and cover some quick attacks you can hit during the transition.
Here's the most basic version, and a great "home base" to start working on some fancier stuff. Start with a basic judo-style collar and sleeve grip. If you're holding your partner's right sleeve with your left hand, plant your left foot in their hip. This will help you keep them at bay during the next part. Now sit down, and while sitting, pivot as much as you can so that your head goes in the direction of your sleeve side (and where your foot is planted). This will allow you to climb your hips up considerably higher, preventing your partner from establishing a combat base position, and ending up in your closed guard.
Ko Uchi Feint
One issue you are likely to encounter while trying the basic guard pull is that your partner's right leg will be too far forward, making it logistically difficult to get your right foot on their hip without them either grabbing your leg or establishing a knee up on the way down. Here is where the ko uchi gari feint comes into play. Try for an inside trip on their lead leg. When your partner reacts by stepping back, they'll give you the space you need to get your foot up on their hip. From here, it's just a matter of following the previous steps.
Starting with that same ko uchi gari feint, once your partner reacts backward, plant your foot on their hip as before. This time, when you sit, scoot your hips a little further under your partner, and try pulling them forward with both upper body grips. If your partner's weight is forward, it will be easy to take them overhead, and you can make this even easier by planting your right foot on their hip as well. Try to establish full mount once you land on top (if you just end up in their guard, you are still generally awarded two points in a sport BJJ context, though).
Yoko Tomoe Nage
Another simple variation here is to exaggerate your head placement even further toward their foot, and then elevate them over your head. Use the same off-balancing concepts from before, but this time just shoot them up over one of your legs. When you come up on top here, you'll probably have more success going to knee on stomach (as opposed to full mount) due to the angle. Alternatively, you can extend your left leg and go for an uke waza sacrifice throw (shown at the end of the video).
The Big Picture
I come from a wrestling and judo background, so it might surprise you that I emphasize properly pulling guard, but I came to two realizations over time. First, it's great to understand what people are doing when they sit to guard, so you can pass, or at least not get caught in closed guard (or submitted or swept!). This is reason enough to understand any "modern" or "sport" BJJ concepts you think you might never use. Second, I also decided that when I was competing in jiu jitsu, I was going to use jiu jitsu as much as I could and try to win that way. Of course, takedowns are a huge part of the game, but I also had a strong competitive advantage over most people I competed against initially (predominantly at white and blue belt) due to my background. It's up to you whether you want to become "one of those butt floppers", but the knowledge is useful, and it's here for you! As always, let me know if everything makes sense, and if you have some success with these techniques.