Lyman-Break GalaxiesLyman-Break Galaxies are selected by performing deep imaging in three broad band filters (Ultra-violet, Green, and Red) as illustrated in the figure. Starforming galaxies at redshifts z>2.5 will be very faint or absent in the U-filter since for z>2.5 this filter is sensitive to flux from the blue side of the Lyman-limit in the restframe of the galaxy. Very little flux is emitted from the blue side of the Lyman-limit since, 1) very few stars are hot enough to produce so energetic photons, 2) photons from the blue side of the Lyman-limit can ionise neutral hydrogen (the definition of the Lyman-limit) and hence stand a good chance of being absorbed, and 3) such photons may also be absorbed by hydrogen clouds along the line of sight from the galaxy to the earth (mainly in the Ly-α resonance line).
This technique has been implemented and used very successfully by Steidel, Hamilton, Pettini, Dickinson, Giavalisco and their collaborators to collect a substantial (>1000) sample of star-forming galaxies at high redshifts. Here is a link to Steidel's page on the Lyman-Break technique. See also Mauro Giavalisco's article on Lyman-Break galaxies. Another interesting contribution to this subject can be found here. The full CalTech LBG survey is available here.