How best to accelerate vast accumulation of merits? If the requisites for attaining the path of a stream-enterer is to accumulate merits and having favourable conditions, what are the best ways to gain merits and having all the necessary conditions to achieve this?
Ways to earn merits:


Practice the Buddha's teaching. 
Practice Dana.
Practice daily meditation and share the merits with all beings.
Support the Sangha or better yet, become a Bhikkhu/Bhikkhuni.


With every wholesome deed one gets closer to Nibbana. 

With every unwholesome deed one gains distance to Nibbana.