Coltrane's Giant Steps is a "don't try this at home" tune. This is the "black belt" level in jazz improvisation.
What makes this song so difficult? The song has a brilliant architecture that makes it sound almost normal. When you look under the surface, it is anything but normal.
You can think of it as two separate tunes. the first part is measures 1-7. Aim for the "landing points" at the Ebmaj7 and Bmaj7 chords in measures 3 and 7 respectively.
The second part goes from measures 7 through 15. This is quite similar to the bridge in "Have You Met Miss Jones". We have a series of ii - V - I sequences. Just to make things a little more challenging, Coltrane raised each of these ii-V-I sequences by a major third, which may feel a bit awkward. The landing points (the I chords) are Ebmaj7, Gmaj7, Bmaj7 and Ebmaj7. Eb, G, B, Eb is an augmented chord. Four major-3rds in a row. Those are the giant steps Coltrane was talking about.
If you are new to this tune and finding it overwhelming, try improvising ONLY on the yellow "landing point" measures: 3, 7, 9 11, 13, and 15 -- and literally sit out the other measures and just count rests. Those landing points all happen to be Maj7 chords, which helps.