Restriction enzymes, how are the recognition sequences determined?
This paper describes a simple method to determine restriction sites, which was used to determine the restriction sequence of the previously uncharacterised enzyme from Haemophilus gallinarum. 

In short, a known sequence of DNA (from the phage $\phi \text{X174}$) is partially digested with the restriction enzyme, and the various digested fragments can be used to determine the relative distances between each of the restriction sites. 

Then, the restriction fragments are extended using T4 polymerase and sequenced using $^{32}\text{P}$ labelled Sanger sequencing. 



Once the restriction map of the enzyme on the known DNA sequence is completed, the individual fragments can then be checked for similarities. For example, HgaI has a recognition site outside of the restriction site. Therefore, when the individual restriction sites are compared, it can be seen that all of them have the recognition site GACGC.