Electrocyclic reactions are always governed by those rules based on orbital symmetry. The pattern is regular though, depending on how many electrons are involved. For example, a 6 pi electrocyclization (hexatriene to cyclohexadiene) will always be disrotatory. Then it alternates from disrotatory to conrotatoryas you add pairs of electrons. I remember this as "3D," meaning if there are three electron pairs (6 pi electrons) then it is Disrotatory. Then it goes on to 4C, 5D, 6C, etc.
For drawing HOMOs and LUMOs, you can use a similar trick. Take the number of pairs of pi electrons and substract one. That number will be how many nodes are in the LUMO. So, for hexatriene, you have 3 electron pairs, 3 - 1 = 2 nodes, which will bisect the sigma bonds between the olefins.
I hope these tricks help.