After school, I go to an English school to study conversation.

Literal

After-school, English-conversation [object-を] learn-[purpose-に] English-school [to-へ] am-going

習い (the verb stem of 習う) + に + motion verb (行く) expresses purpose: 'go in order to learn.' ~ています marks an ongoing habitual action — not 'going right now' but 'regularly go.'