Following chart may come handy while translating western notes of any tune or song into Indian Sargam, and vice-versa.

ScaleCDEFGAB
IndianSaReGaMaPaDhaNi
WesternDoReMiFaSoLaTi

The letters in all the above rows (column wise) generally follow a sequence.  For example, if we start the scale at F, then the sequence would be FGABCDE, or when at B, it would be BCDEFGA, and so on.

Sa Re Ga Ma Pa Dha Ni and Do Re Mi Fa So La Ti remain constant.

Every musical instrument can be tuned to a certain scale.  With the above example, we would be playing Sa at C scale.

Following table [suggested by Vikram Jamwal] can be used as a key to play Sargam on Western Instruments and vice versa:

Scale ↓SaReGaMaPaDhaNi
AABC#DEF#G#
A#A#CDD#FGA
BBC#D#EF#G#A#
CCDEFGAB
C#C#D#FF#G#A#C
DDEF#GABC#
D#D#FGG#A#CD
EEF#G#ABC#D#
FFGAA#CDE
F#F#G#A#BC#D#F
GGABCDEF#
G#G#A#CC#D#FG