The method is described in full in the American Journal of Human Genetics.
However, very briefly, the method first assesses patterns of local LD by calculating a matrix of local pairwise correlations between SNPs. Row i of this matrix will indicate to what extent the signal of SNP i is replicated by its neighbouring SNPs, and the sum of these values will reflect the total amount that the signal of SNP i is replicated. Based on this matrix, LDAK determines SNP weightings so that the sum of the values in Row i times the SNP weightings equals (approximately) one. Then, using these weightings, LDAK calculates an adjusted kinship matrix where the (relative) contribution of each SNP is determined by its weight. Without these weightings, genetic variation tagged by many SNPs will have an exaggerated effect when calculating genetic similarities; with these weightings, each independent genetic signal should contribute equally.
When calculating weightings, LDAK can model how LD is expected to decay over distance. Following this paper, we now recommend that this option is not used for population datasets (where most individuals are unrelated), so since LDAK3 this feature is turned off by default. However, the feature should be used when analysing pedigree datasets or animal/plant data where there are many pairs of closely related individuals.