Use of restriction endonucleases to analyse Variable Number Tandem Repeats (VNTRs)
The general situation regarding using restriction endonucleases to analyse Variable Number Tandem Repeats can be explained with (as well as without) reference to the illustration below.

The original region of DNA in which the insertion occurs will in general be complex (rather than repeated) and conserved to a reasonable extent among H. sapiens. The complex conserved sequence is represented by a gradient of colour in the upper part of the diagram so that the point at which the original copy of the repeat inserted can be identified in different individuals (or alleles), A, B and C, where, for the sake of argument, two, three and four copies have been generated.
The individual repeat unit is relatively short (typically 10–100 bp), so it is relatively easy to find conserved sites for at least one commercially-available restriction endonuclease on either side of the original insertion, but not within the repeat.
The mathematics of this reasoning are quite simple, and I provide exercises on my University website. However, as an example, consider a 4-base pair sequence that is the target for a restriction enzyme. It need not be palindromic, but as most Type I restriction endonucleases are, let’s choose GGCC. The chance of finding this in any tetra-nucleotide is 1 in 256 (4x4x4x4), or, in other words, it should occur in any 256 bp stretch of DNA. (Of course this is just an average of what may be a normal distribution, and overall base composition will affect the actual frequency.)
The net result will be that it will be possible to generate fragments of an overall size such that the flanking regions are not so large that they make it difficult to distinguish differences reflecting different numbers of repeats.
And today?
The polymerase chain reaction (PCR) might well be used instead of restriction endonuclease digestion as, given that the DNA sequence of the region has been determined, one could choose appropriate positions in the flanking regions to generate DNA fragments for analysis. See, e.g. Richie et al. (1999).