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The basic idea for these approaches is to first create a "cyclical" world with at least 2 full cycles in each dimension. This can be either in terms of texture or geometry. For example, to create an infinite forest of geometric trees, first create a patch of trees that's roughly square and random looking. Then tile that pattern so that there are at least two copies in the X and Z direction. Then, at any point in time you can transate the user's eyepoint by exactly the width of the patch in either X or Z and there will be no apparent change in the scene. The only thing visible might be trees that are beyond the tile pattern visible in the next. You can alleviate this by either using fog to limit visibility or build a 3x3 or 4x4 tiling (instead of 2x2) and always keeping the user near the middle.
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