Apologies if this is super obvious, but...
If there is a weak Civ (with a handful of cities) nearby at the beginning of Age of Exploration
1. Rush to study Piety. Pick Brahmanism (+ 2 relics for first-time conversion of a Capital)
2. Build a Temple
3. Train a Missionary
4. Convert their Capital (+ 2 relics)
5. (Declare war and) capture the Capital
After you capture the Capital, one of their remaining cities becomes a new Capital. Repeat steps 4 and 5 (you can move a missionary ahead of time if you can predict what the next capital will be). If you see them sending out settlers and don't care about the penalty for razing cities, you can feel free to ignore them and let them found new cities to keep the chain going. Otherwise, you'll need to watch out for the settlement limit.
Bonus tip: if you are running out of slots for relics, buy a temple in one of your towns that can specialize and switch it to Religious Site to get two relic slots fairly pain free.
If there is a weak Civ (with a handful of cities) nearby at the beginning of Age of Exploration
1. Rush to study Piety. Pick Brahmanism (+ 2 relics for first-time conversion of a Capital)
2. Build a Temple
3. Train a Missionary
4. Convert their Capital (+ 2 relics)
5. (Declare war and) capture the Capital
After you capture the Capital, one of their remaining cities becomes a new Capital. Repeat steps 4 and 5 (you can move a missionary ahead of time if you can predict what the next capital will be). If you see them sending out settlers and don't care about the penalty for razing cities, you can feel free to ignore them and let them found new cities to keep the chain going. Otherwise, you'll need to watch out for the settlement limit.
Bonus tip: if you are running out of slots for relics, buy a temple in one of your towns that can specialize and switch it to Religious Site to get two relic slots fairly pain free.