You always hear people saying that you should do abs slow and under control with correct breathing, but i recently attended a ab class and everything was rigorous and fast place. So what is the best way to see improvement in abs?
You want each repetition to be deliberate, meaning slow and under control. Every ab exercise is going to involve you bringing the sternum towards your pelvis. If you're not doing this, you're not doing an abs-specific exercise.
I'm not knocking your ab class, but just because it's a class and even if it's a certified personal trainer, that doesn't always necessarily mean you're getting taught correctly.
You have to diet to lean up enough if you want to see your abs, but as far as getting them solid, it's all about consistent, smart training. I usually do abs no more than 3-4 times per week at around 100 total reps per session. But I don't do them fast and choppy, I do them under control and squeeze at the top. Also, after each set do some stomach vacuums. Feels great.
Also, for obliques, check into side bends (where you put a light bar over your back, bend forward slightly, keep your pelvis still and rotate at the waist). Don't use weight though.
But it's mostly about consistency.
Sounds more like a core conditioning class.