In general, there are the following methods of removing sins:
SwApanena anutApena tapasA adhyayanena cha |
pApAt tathA dAnena cha apadi ||
Manu Smriti 11.227. By confession, by repentance, by austerity, and by reciting (the Veda) a sinner is freed from guilt, and in case no other course is possible, by liberality.
So, we have 5 methods. And, among these the "adhyayana" method (recitation of Holy texts) is the one you're referring to (chanting mantras like Om Namaha Shivaya). Also doing regularly PujA will come under medium kind of austerity. Fasting is another kind of austerity. (But, these don't give instantaneous results. One needs to keep doing them for many days.)
And, all these methods are effective.
Manu Smriti 11.228. In proportion as a man who has done wrong, himself
confesses it, even so far he is freed from guilt, as a snake from its
Manu Smriti 11.229. In proportion as his heart loathes his evil deed,
even so far is his body freed from that guilt.
If you want the quickest method then that probably will be one among charity, confession and chanting. But for chanting one needs to be qualified to do the chant. For charity and confession, on the other hand, everyone is qualified.
Also, this is Kali Yuga, and scriptures clearly mention that in this Yuga the charity method works better than the other ones.
Tapah param krita yuge tretAyAm jyAnamuchyate |
yajnamevAhuh dAnamevakalau yuge ||
" Self-mortification is the rule in the Krita age ; knowledge is said
(to be the same) in the Treta ; in the Dvapara, (they) say sacrifice
(to the gods to be) the sole (rule) ; and charity alone in the Kali
ParAshara Smriti 1.23
Besides all these, one other method that the PurAnas suggest, is nAmaKirtana or chanting the Holy names of Gods. That is also said to remove sins quickly and effectively.