We describe a new approach to obtaining very high surface densities of optical spectra in astronomical observations with extremely accurate subtraction of night sky emission. The observing technique requires that the telescope is nodded rapidly between targets and adjacent sky positions; object and sky spectra are recorded on adjacent regions of a low-noise CCD through charge shuffling. This permits the use of extremely high densities of small slit apertures (`microslits') since an extended slit is not required for sky interpolation. The overall multi-object advantage of this technique is as large as 2.9x that of conventional multi-slit observing for an instrument configuration which has an underfilled CCD detector and is always >1.5 for high target densities. The `nod-shuffle' technique has been practically implemented at the Anglo-Australian Telescope as the `LDSS++ project' and achieves sky-subtraction accuracies as good as 0.04%, with even better performance possible. This is a factor of ten better than is routinely achieved with long-slits. LDSS++ has been used in various observational modes, which we describe, and for a wide variety of astronomical projects. The nod-shuffle approach should be of great benefit to most spectroscopic (e.g. long-slit, fiber, integral field) methods and would allow much deeper spectroscopy on very large telescopes (10m or greater) than is currently possible. Finally we discuss the prospects of using nod-shuffle to pursue extremely long spectroscopic exposures (many days) and of mimicking nod-shuffle observations with infrared arrays. ; Comment: Accepted for publication in PASP; 25 pages, 12 figures. A higher-quality compressed Postscript file (2.2Mb) is available from http://www.pha.jhu.edu/~kgb/papers/nodshuffle2000hq.ps.gz