I've been given a Trek 4300 mountain bike by my dad. I usually ride a road bike. After my first ride I'm sure I need to reduce the springiness in my from forks. There are two dials there labeled RST preload. They are tight, but I can turn them. I tried 360 and 720 clockwise and anticlockwise, but couldn't tell which way was correct. I see that other bikes allow air in here, so maybe I need to flip these off. Can anyone advise?
The 4300 came with a very basic suspension. As such it has very basic adjustments. The preload adjustment makes the spring feel stiffer by slowing the initial compression of the fork. There is no dampening or rebound adjustment which would control the speed at which the fork extends after it compresses. What you may be experiencing is the lack of rebound control. The preload is at its' max with the knob screwed in or turned counterclockwise until it stops. It is possible that either the knobs are broken or the fork has worn out if you see no difference with different settings. Unfortunately there are no parts available for these. Your bike has a 1 1/8" straight steerer tube which is no longer used on higher quality forks. So your options are limited to looking for a older used fork or replacement with a size adjusted rigid fork.
The answer very much depends on what type of fork you have, and where its control knobs are situated, if at all present.
The main tunable parameters a suspension fork has are sag, compression and rebound. The latter one corresponds to how fast the compressed fork goes up, which may correspond to what you describe as "springiness". Often, but not always, the rebound control(s) are placed under the fork, near the wheel's axle.
From what I can say, the bicycle in question has "Spinner 300 Suspension", which is a noname brand. I am not sure that such fork will have a means to control rebound at all.