I've only karted for fun but have had some success.
First thing is that if you stamp on the brake, you will spin. Normally this happens when someone in front spins and you automatically jam on your brakes. Try to resist just stabbing the brake on.
The kart will corner faster than you will imagine at first, but tyres do take a while to heat up so for your first lap or two be aware that it may slide all over the place.
As already said, stay smooth & try not to spin/crash. You will generally do better by staying out of trouble.
Use the whole width of the track – if you use Out-In-Out on the corners & use the whole track, then you will be able to corner quicker – you always see people not using the whole track & it slows them down.
Last time I went karting it rained for the last 15mins. It was the first time I had karted in the wet. I found the fasted way was to approach a corner and turn in, jab the brake to break traction, the kart will begin to spin. Apply opposite lock quickly and get back gently on the power to slide round the corners. I was about 5s per lap faster than the nearest driver doing this….
And have fun!!
Take your own gloves – use your mountain bike ones if you can as they will be much more comfy than the ones they provide. And if you are a shorty like me, then ask for a seat bolster or you will struggle.