The abbreviations are that the initial number is the number of rings (e.g. "2-" replaces "bicyclo") and the terminal alkane (e.g. "decane") is omitted as the number of carbons is easily calculated (sum of the numbers in the square brackets + 2). Thus decalin would be "2-[4.4.0]".
For monocyclic systems the single number in the square brackets indicates the ring size, e.g. cyclohexane is "1-[6]". For acyclic compounds the single number in the square brackets indicates the longest linear chain, e.g. butane is "0-[4]".
For spiro ring systems the IUPAC Nomenclature for Spiro Compounds is followed instead or as well.
If two (or more) ring systems are linked by an acyclic linker(s) both (or all) ring systems are defined separated by the linker(s). For monocyclic rings the attachment point is number 1 and need not be given (e.g. "1-[6]-CH2-1-[5]") but for polycyclic systems the numbering of the attachment points need to be given e.g. "2-[4.4.0]-2-CH2-2'-2-[4.3.0]".
The numbering of the ring systems is as described in the IUPAC nomenclature (which will be different from the numbering in the cyclisation column as that numbering is derived from the precursor molecule). If two or more ring systems are present the second specified ring system gets primed numbers (e.g. 2') and the third one gets double primed numbers (e.g. 2") etc.
The abbreviated name for the ring system(s) is followed by the substituents attached to the ring system, starting with the ones that would normally be suffixes, e.g. "-2-en-5-ol", and then the ones that would normally be prefixes, e.g. 7-oxa-3-iPr-6-Me (abbreviated names for the substituents are used wherever possible). An alkylidene group is indicated by an equals sign, e.g. a methylene group on C-5 is given by "5=CH2". Other reasonably simple substituents can be defined by the atoms, e.g. "4-CH(OH)Me" but larger groups can just be given as "-R".
If multiple substituents of one type are attached the "di", "tri" etc. is omitted as the number is indicated by the preceding numbers, e.g. "3,5,5-trimethyl" is given as "3,5,5-Me".