How can I smoothly transmission into lower gear? For example

If you let out the clutch slowly it won't jerk as much. That's what I do, at least.
>tfw still trying to shift from 1st gear into 2nd without jerking really hard

Rev up the engine to as near as you can estimate the revs will be once the clutch is engaged on second gear. Say you are traveling at 50km/h in third, at 2200rpm, to slow down, let off the gas and disengage the clutch. Revs will drop to idle. Put it in second gear. Rev up to about 3500rpm no need to be exact the first time, just give it 33%-75% gas for an instant once you feel and hear the revs jump get off the gas. Now release the clutch pedal to engage the clutch.
Practice makes perfect. No need to brake to slow down in normal traffic using this, but if for some reason you want to drive fast, you need to do all this while also braking and maintaining stability throughout since you are approaching a turn.