How do you reach 100 Brachos on Tisha B'av? You can't smell spices See Here, like some do for Yom Kippur, you can't eat, and you probably won't be going to the bathroom too much. So, how do you reach 100 Brachos on Tisha B'av?
Listen to the blessings of the chazzan, the blessings on the Torah and haftorah.
According to one opinion mentioned in Mishnah Brurah O.C. 124:4 - see Mishnah Brurah commentary #20 - someone who answers "Amen" to the Chazan's repetition of Shmoneh Esreh is considered as if he had said the blessing himself.
There are 5 occurrences of Shemoneh Esreh from Ma'ariv through mincha, if you include the silent and the reptition. That's 95 blessings. Add the 22 blessings from the beginning of Shacharit, and you're well over the 100 needed.
If you don't go to shul, I counted 92 - 93 brachot. For the other 7, put on an extra few pairs of tzitzit, or, as my wife tells me, "you have to go the bathroom whether you realize it or not!". When you're done, you'll say *Asher Yatzar" (and maybe, thank your wife, too.)