The left hand technique for stride piano involves playing two parts at the same time. The little finger plays a bass note, then you move your hand up an octave and play a chord that goes with that bass note. This technique seems awkward at first, but with practice it feels automatic. Most beginning stride piano players drill with left-hand exercises that break up chords into bass-and-chord patterns.
In stride piano, the right hand plays chords between the beats the left hand is playing. In music terminology, this is often called a "push." The right hand pushes the chord a little ahead of the left hand. In actual playing, this sounds like the right hand plays the chord just before the notes of the left hand, creating a "stride" feeling.
After you have some proficiency at playing right hand chords between the left-hand beats, you can start leaving gaps. Skip some of the right hand chords. This surprises the listener and maintains interest with a choppier rhythm.
You want to progress to the point where the right hand plays melodies. You can break out of the chord rhythm and start playing melodic phrases with the right hand. The left hand maintains the steady stride of the octave-chord pattern, while the right hand is free to play single-note melodies.
When you get used to divorcing what the right hand is doing from what the left hand is doing by playing melodies, you can advance to improvisation. The right hand can begin to explore new melodies that fit in with the chords, yet offer new melodic and rhythmic inventions. These improvisations cannot be studied, they have to come from your taste and personality.