Hi ms.lee chan;
welcome to HealthcareMagic
To know that fallopian tubes of a female is blocked there are 2 methods:-
1-To do a HSG(Hysterosalphingography) that is to insert a dye through a canula in the uterus
and when the dye is pushed X-ray is taken to see if the dye is coming out of the tubes ;it is done in a X-ray dept of a pathology.
2-To do a Laparoscopy
from above that is abdomen and from vagina again a canula is inserted and dye is pushed and it can be directly seen by a doctor whether the dye is coming out of the tubes
These test prove whether the tubes are open or closed and most of the time the tubes get opened when the dye is pushed if there is a simple block in it .For details regarding the treatment with or without surgery please discuss with your doctor.