Here's how I roll:
(rewritten for 1.06)
1. Start a Grand Campaign as Denmark. Hard/Simulation. Denmark because being far from India it's easier to time convoys to arrive at their destination when there's 1800t merchandise ready there.
2. Build a Schooner, load your Cutter with best export goods you can and send it to India. Where in India? Check the ledger prices for your export goods and see where they will sell best. Send Cutter there. When Schooner builds start another fleet, load with exports and send to India. You should do everything to get a Salesman captain.
3. When Cutter reaches India you will get 50 000 credits for that. Load it with import goods and send back home. Time its arrival in Europe with your Schooner's arrival in India. Try to trade Tea or Silk this few first runs and always send to a port your exports sell best.
4. Cutter should never go to India again, it should stay in Europe hoping to get a mission or two to finish or make a Ivory/Gold/Diamonds run once in a while if prices are high and you have some cash to invest in such a trip. Later you can add another Cutter to this fleet and go hunting AI ships if you're good on tactical level. Becoming a pirate company pays well (stolen goods from ships coming back from India as well as ships themselves if you can board them or make them surrender) but is also risky so if you go for it, try to not fight more than one AI faction at once.
5. Keep adding Schooners until you have a fleet of 5x Schooners bringing each Tea, Spices and Silk to Europe. Also try to gather 400-500t Iron Wares in home Warehouse for later. If you get a mission to conquer an Indian port, ignore it completely. It's 15 years too early to start conquering and if it's on Hard, you can't afford paying upkeep for a port anyway.
6. Stay out of diplomacy for now. If you propose a deal, AI won't like it. If AI proposes a deal, they will try to bribe you into accepting it right away. You can earn many thousands by waiting for AI to approach you.
7. When your Schooner fleets are ready, you should start looking into building a war fleet of 5x Galleons. Start around 1615-1617. When they are ready first send your captain to hunt pirates until he learns skills Conqueror and Organizer. This will allow to load more marines on ships and also use them better.
8. Use that war fleet to conquer 3 ports in India and use tools you gathered in Europe to upgrade Trade Posts in them to level 4 immediately. If they have any other buildings, demolish them. You want ports with level 4 Trade Post, level 1 Warehouse, no Shipyard, Fort level 1 and Garrison level 2 (level 4 after 1630).
9. If you are short on cash for upgrades, conquer a bunch of ports in Africa and sell them to AI companies for around a million pounds each. You are very poor at this moment if it's Hard difficulty but you should start booming economically very soon with cheap goods and cash influx from selling ports to AI. Don't keep any ports in Africa for yourself unless you're playing on Easy or Medium and on Hard only if you are very lucky or exploit price changes.
10. When you have ports and they are upgraded it's time to start moving to some heavier convoys, Pirates must have started attacking your Schooners already. Go for fleets of 1x Galleon and 4x Flutes per each port you own with Silk, Spices and Tea and a fleet of Brigs and left-over Schooners to haul Coffee and Porcelain. Also keep a fleet of 1x Brig and 2x Xebecs for errands and piracy (if you do that).
11. Around 1630 you should consider adding Frigates to your main India convoys to escort your pretty weak Flutes. In 1650 you should switch Flutes for much bigger and stronger East Indiamen. In 1670 switch Frigates leading your convoys to SOL46s. 1x SOL46 + 4x East Indiamen is a perfectly balanced trading convoy and will serve you well for the rest of your game.
12. All your convoy captains should be at least Salesmen and Hagglers. Hire them at young age and send them to hunt Pirates with your "errand" fleet giving them those crucials skills before you give them convoys to run. It will multiply your incomes many times.
13. If you don't want a major offensive from AI companies, don't monopolize any good or region. By 1650 I usually own 2x Tea ports, 2x Spices, 2x Silk and 1x Porcelain. Later I add a Coffee port to that (moderate profit on medium, low but steady profit on hard) and also Mozambique (best location to hunt pirates from). Fleets that serve ports in Africa I set to "cautious" mode (blue face icon) so they travel extremely slow and give prices time to recover. India convoys I count on quantity and salesmen captains, it's enough even on hard.
14. The above setup of ports with Flutes hauling goods and your fleets killing pirates and pirating AI companies should be more than enough to finish requirements of the grand campaign way before their time runs out. Just make sure you don't upgrade port defenses too much and don't run your main convoys on cautious mode since both things can quickly bankrupt you. Also avoid owning too many ports in Africa. Paying for Pacts with AI companies to secure all the "hops" to your home port is way cheaper than running those ports on your own
15. If AI owns many Gold and Diamonds provinces, you can park a pirating fleet next to them and get tons of that stuff for free. ARRRR.
Voila. Comments most welcome.