Fana means annihilation or passing away, and in Sufi usage it names the extinction of the ego-self so that the mystic perceives nothing but God. It is almost always paired with baqa, subsistence or abiding, the state in which the practitioner returns to ordinary function with the transformed awareness intact. A Sufi who reached fana and did not come back would be, in the tradition's own terms, incomplete: the ideal is the one who is with God inwardly and with people outwardly.
The path to it is not an experiment. Sufi orders prescribe a graded discipline under the direction of a shaykh: repentance, scrupulousness, renunciation, poverty, patience, trust and contentment as stations to be traversed, with states given rather than achieved along the way. The central practice is dhikr, the remembrance of God by repeated invocation of his names, performed silently or aloud, alone or in assembly, sometimes with breath control, music or movement, as in the turning of the Mevlevi order. Practitioners are warned repeatedly against pursuing experiences for their own sake, and the literature is full of cautionary accounts of those who mistook a state for an attainment.
The theological account of what happens is careful. What is annihilated is the practitioner's attributes and self-will, not their created being; what remains is God, who was always the only reality. Junayd of Baghdad, whose sober formulation became normative for much of the tradition, described a return to the state one had before creation, and insisted the mystic remains a servant throughout.