Note: the structure described below is very general; different schools of Hindustani music may follow slightly different styles, and indeed different singers will have different styles. This is only a vague outline.
The khyal is one of the two main forms of Hindustani music, the other being the dhrupad. Both share many characteristics, particularly since the khyal is derived from the dhrupad; however, the khyal places more emphasis on free improvisation, whereas the dhrupad places more emphasis on careful and elaborate exposition of the raga.
The beginning of the khyal usually consists of a few minutes of unmetered phrases to give the listener an idea of the flavour of the raga. Following this, the singer commences the vistar or badhat section. This is the main section of the khyal. In this section, the singer chooses a song in slow (vilambit) tempo. This song will have some basic tune to it, but the majority of the performance will be improvising a tune to the words. A beat cycle in this section will usually be anywhere from 60 to 90 seconds long, and the sam, or first beat, falls in the middle of a phrase. So within the beat cycle the singer may improvise however he wishes, provided that when he hears the sam approaching he begins singing the first phrase, so that on sam the tabla and the singer synchronise. After the sam the singer may wander off on an improvisation again. This cycle repeats indefinitely.
After the vistar comes the chota khyal. This is another song in the same raga, but in fast (drut) tempo. The emphasis here in on fast, rhythmic improvisation interspersed with bits of the song. There are three types of improvisation in this section: melodic improvisation with the words of the song, bol tana; with the long 'a' sound (akar); or with the names of the notes (sargam). This section is usually in the region of 5-10 minutes long and culminates in the climax of the song as the tanas (improvisations) get ever faster and more complex. At the end of the song, the tabala stops playing and the singer may go on for a few moments with unmetered phrases, much as he did at the beginning of the song.
Sources: The Raga Guide, ed. Joep Bor. Published by Nimbus Records with the Rotterdam Conservatory of Music.