The exposition will usually be composed of a first group (in the tonic key) and a second key (in the dominant, if major, or the relative major if in a minor key to start).
The orchestral exposition would give the outline or the skeleton of the themes and the piece, and then when repeated by the soloist, they would change keys and give the full version with all the themes (minus the ritornello).
The development section commonly starts with material that directly relates to the end of the exposition section, in order to make the move between the two sections smooth and joined, and you would rarely find a deliberate break or rest between the two. This section usually develops and explores themes form the exposition in a number of ways, e.g. sequential repetition, elaboration, ornamentation, fugato or elongation and often moves through a number of keys, unlike the exposition that usually transitions only once. Another common technique is to start the development in the relative (or parallel) minor of the exposition (An exposition in C major would render a development section in A minor, etc). Further on in the development, there is often a build up of themes and ideas and then their break down, usually named the fragmentation. Overall, the harmony in the development is chromatic compared to the exposition. Simple chromatic chords in the exposition would here be expanded to temporarily prolonged chords.
The recapitulation restates the themes of the exposition, usually in the same order, but usually all in the same key, the tonic. This section fuses both the soloist exposition and the orchestral exposition, often using all the themes. Although there is fusion, the ritornello still occurs, and there is still soloist elaboration of some orchestral themes (through antiphony and imitation). The themes in the recapitulation section are often altered in some way, sometimes through truncation, or sometimes they are elaborated or lengthened. Another common technique is to expand the final cadence.
The cadenza is the part of a concerto where the soloist is unaccompanied and shows off his or her skills on the chosen instrument of the concerto. In early sonatas, this cadenza would be improvised or elaborated on the themes of the exposition, without score. As the classical era progressed, however, the cadenza started to become scored, and just played from the music by the soloist. The cadenza was often written by the composer himself, but was also sometimes written by other composers. This section would always end with a trill, so as to tell the orchestra when to come back in with accompaniment.
The coda would begin when the recapitulation has ended. In early sonata forms, there would be a series of codettas, but later on this section became larger, usually quite lengthy and similar to the development section. The coda always has a very strong perfect or plagal cadence at the end, finishing the movement (or piece) off.