One of the types of signals for which the LIGO interferometric gravitational wave detectors will search is a stochastic background of gravitational radiation. We review the technique of searching for a background using the optimally filtered cross-correlation statistic, and describe the state of plans to perform such cross-correlations between the two LIGO interferometers as well as between LIGO and other gravitational-wave detectors, in particular the preparation of software to perform such data analysis.