If the dataset consists of regularly spaced data with no points having bad quality then the best results will be obtained using the standard FFT algorithm in the application POWER. This is quick and accurate.
For data containing gaps or uneven sampling you must use the aplication LOMBSCAR, which employs the LOMB-SCARGLE algorithm, or possibly, SINFIT, which performs a least squares fit of sine waves to the data.
The document USER_006 also gives an account of the performance of a CLEAN algorithm. This is available from Harry Lehto at Southampton (username: hl@phastr.soton.ac.uk). Interested users should contact him directly.