Unfortunately, many people have analyzed this piece, but the Bartok seems way to hard and all I have with me here is the Burkhart anthology.
Anyhow, the two motives of significant importance, it seems to me, are m. 1-2 (motive 1) and 3-4 (motive 2) in the right hand. Most of the rest of the piece can be analyzed as some form of those two ideas.
For example, mm. 7-10 in the right hand are just a development of motive 1 (played again in the right hand). After that, the left hand begins to play with motive 1 much like the right hand had been doing, while the right hand plays a new idea twice in a descending sequence (m. 11 & 13). The left hand continues playing motive 1 until m. 18, when I hear a major structural phenomenon: a PAC in F major.
After this, the left hand continues with motive 1 until measure 22, when it plays the idea from the right hand m. 13, repeating it in a sequence one step down. At this point (m. 22), the right hand again picks up with motive 1, this time inverted (I believe). The music is then very much like m. 13-21, except there is a textural inversion - this time the left hand accompanies the right.
The next structural phenonenon occurs in m. 38 with a PAC in A, though the tonality quickly shifts into a developmental section that wanders from key to key (g minor then F major) before arriving solidly in d minor again in m. 44 with motive 1 in the right hand and motive 2 in the left. The piece approaches a cadence in m. 49, but deceptively resolves to Bb (the relative major) before winding its way back to d minor for the end.