the main harmonies that are used are the octave and the thirds so with octaves ones plays a note and the other guitar plays it an octave higher at the same time , the other one is that one plays a note and the other plays the third of the scale starting from the note the first guitar plays
so for example first plays C (cmajor) then the other must play E and this gives a nice harmony , you can also make it E and G in c major etc just as long as you take the third note in the scale starting from the note.
an example of this harmony is in the interlude of master of puppets where james and kirk play a little melodie that is harmonized with those thirds , you could
also do this with other notes off course , this will just give another sound, but the main used are those i mentioned
and the song you mentioned , they play in the same key , i think it's c#minor and the song uses the thirds i just explained
i'll explain it using the song
first of all c# minor is C#-D#-E-F#-G#-A-B-C#
i'll do only a small part of the twin harmony thing (since it's all the same idea)
(donno how this is gonna look like when posted)
it's all on the highest string
Guitar 1:
1:|---12---11----9--------9---9-9---11----9---
2:|------------------------------------------12
------E----D#---C#--------C#---C#---D#----C#-B
let's say you got this part and you want it harmonized , then you can either have your other part higher or lower then this one , in the song the other one is lower
remember the notes you got in the previous
and notes of c# minor C#-D#-E-F#-G#-A-B-C#
(i'll explain later what the * means, why it is E and not A (still third difference though)
------E----D#---C#--------C#---C#---D#----C#-B
the notes of the second guitar are :
------G#---F#----E*--------E*---E*--F#----E*-G#
they get there to take from the first guitar the third so E passes to F# and then to G# , normally this is all the difference between the harmonies but here they lowered the harmony note an octave so they combine the third with the octave harmony
in tab this is
Guitar 2:
1:|--------------------------------------------------
2:|----9----7----------------------------------------
3:|---------------9-----------9---9-9---11---9----8--
-------G#---F#-----E*---------E*----E*---B--E*---G#
if we would put those two guitars together we get
1:|---12---11-----9--------9---9-9---11---9----------
2:|----9----7----------------------------------12--
3:|---------------9--------9---9-9---11---9----8--
------G#----F#----C#--------C#---C#---D#--C#----B
------C#---B-----E-----------E---E----B---E*----G#
again resumed :
*so with C# they went up to the third starting from c# that makes the E and then lowered this E an octave , this used a combination of both harmonies i mentioned
so if you want to create a harmony for an existing melody just take the scale take the third note int he scale starting from the note in the melody higher or lower (you can choose) and to this for all the notes in the melody et voila you have made yourself some harmony
ps: i don't know the song from thin lizzy , i just searched for some tab so don't know if the tabs are correct or something
hope something of this makes sense to you
if there are faults in this let me know , it's getting kinda late