How to use East India Company?

I'm really in doubt, how to use the East India Company most optimal. I think it is a hard one to consider, since you only get benefit from it when other makes trade routes to your city. I hope someone can help me, and give some suggestions.
Should I build it in a city with many luxury resources, or in a large city? Are coastal cities preferable?
And should I adopt Merchant Navy (+4 production and +4 culture for East India Company) policy before or after, I build the East India Company?

I'd say that you try to find a good city location which is coastal. A good city location would be to have some different luxuries and/or strategic resources. Preferably next to a river as well to make your trade routes from that city as lucrative they can be (and for the AI). Sadly though I must say that I think the AI mostly ignores if a city has a East India Company. I usually place mine in the city which can make the most lucrative trade routes but I have extremely few, if any, trade routes connected to this city from the AI.

I've read that the AI has been better to make trade routes to such a city after the patch, but I haven't noticed it. I often build the Colossus as well which also grant more gold for trade routes for other players. So from my own experience I would just recommend you building it for the base gold the East India Company grants and dont consider where to place it too much.

It could be that the AI chooses not to send trade routes to a city with the EIC because they don't want you to make a lot of gold out of their TR. In my experience, they prefer to send trade routes to my cities where I only make 2-4 gold from their TR. In a game I'm playing at the moment they connect TR to Mycaene where I make 2 gold per turn instead of connecting to Athens which has the Colossus and more resource diversity.

For your question about the social policy connected to the EIC, I'd that you shouldn't bother with it unless your aiming for the social policy which grants 4 gold extra to naval trade routes. I once took the policy for my coastal Rio de Janeiro which was extremly production starved. Only two hills, so I opened the exploration tree for the extra 7 hammers since I was gaining so many social policies anyway.

Usually the AI consistently brings its trade routes to one or two of your cities, so just put it in the one that already gets most trade - that's probably the one they have the easiest access to. I doubt the AI will actively redirect trade away from an EIA city, even if they don't actively try and trade with it either.

It seems, that the AI not works quite well with the EIC.
But thanks for the advices.

It works well in the capital since its gold yield will be amplified most readily, +25% from tradition and normally one of the first cities to get financial buildings.

Optimal use: Cross ocean routes with Seaport/Harbor that the AI connects to you. They need Navigation/Astronomy etc.

Civ V: The best location of almost all national wonders is always your capital. Your capital will normally have the most gold, science, production, trade routes, etc.

As to the policy question; normally neither; Science is King; which is normally full tradition + 2 filler policies + Rationalism. Normally there are more useful filler policies than left side of Exploration. (If planning on completing a lot of city state quests: Consulates; if happiness is an issue and you have several coastal cities: First right side of Exploration; if wanting more great works; first left side of Ascetics; if just wanting to build some more world wonders any two openers.)