This old site has a few strategy tips:

http://www.strategyplanet.com/dailyimperialist/

- Buy lots of explorers: search your mountains/hills/swamps first, then send them to the minor nations/new world to find stuff :o) (often the point below will give you a start point)
- Send one ship to explore coastlines. Can be a bit of drag on early trading though, so it might have to come home early.
- Do the trade post option with one or two indian nations. Buy whatever they have to sell. Hope the other guys don't invade it before you have a chance to buy plots in each province. This will give you a way to make money later in the game if you haven't found gold/silver/gems/diamonds.

Uh, haven't played in a while, I'll get back to you :op

I've NEVER had peaceful trade with natives pay off. Too much effort, too little payback, too much risk of other powers conquering them.

I've also never really bothered searching for resources within minor nations. It just seems too important to use all your explorers to find the new world treasures as quickly as possible.

One thing that irked me about the game was how you NEEDED bronze for any military but the presence of tin is always so finicky. You can get by with only one source but it almost seems rarer than diamonds.

I usually don't trade much at all. Competing with other MPs in minor nations is a pain in the rear and trading with the natives is even less profitable. Better to just invade the native provinces and ship the good home for free.

As a result I usually use 2 ships to explore the new world. If I find native capitols I try to invade them asap. It gives a nice bunch of cash and you get a free port.

I usually train 6 explorers asap and let them search deserts and mountains with priority for diamonds and gems.

I usually play on hard, and its - hard, even after many games I still lose about a third of the time.

An early spy is key, as is building up food and finding an easily invadable new world nation. I usually delete the useless peasant militia on turn 1, build a second knight when I find a lightly defended (2 tent) minor nation capital and steam straight into it. The money from that gives you the resources to get embassy with a minor nation in the old world to make nice with (pact/mechant/buy up their resources with)

Its worth keeping a third world client nation because you can sell finished goods to them - you reach a point where you produce more than you need, but you always need money - for research and wars. The old world minors will secede or be invaded, you cant trade with them indefinitely.

I love this game because every choice means you are denying yourself something else - it really makes prioritising important. Nothing can be neglected, because without an army, enemies get opportunist, without a navy you can't transport and sell goods, without warships you can't defend your fleet, without workers you can't improve your land.

Just brilliant.

Tips then

Spy, spy and spy some more. 4 is not a waste. Spend as little on research as you can until rich
Prioritise researching Printing Press, University and Horse Artillery. Then convoying.
Conquering minor capitals is really good - and remember they give you the advantage of bureaucracy before you research it, so improve timber to get free lumber in those areas (or whatever you have).
On harder difficulties try to make nice to old world nations, and beef up your army to deter early attacks
Trading is still important - it improves diplomacy, and money is always scarce.
Knights are king til you have horse artillery, them go for muskets. Arquebusiers are not worth it, and pikemen tend to be a desperate defence purchase.
Tin is always scare, start buying it early - the AI opponents go for iron mainly
Have your capital inland (on a river) that maximises your starting fish.

Taking forts

Find the spot that lets you blow a hole in the wall with your mobile artillery without counterattack, then send forward expendable units to trigger counter battery fire until it is safe to send forward mobile artillery. Then focus on destroying their artillery (static or mobile). Cavalry, archers and skirmishers are good fire drawers. Heavy infantry (musketeers and grenadiers) are the best all rounders. You will need to outnumber the enemy, but remember the higher grade of general you have the more troops you can attack with.