Castle Building

Build statue on the first day and start earning extra money. If you're warlock, be quick to build dungeon.
Build well on the first week to get some extra population.
Build all creature structures you can before upgrading them - this way you'll end up with more troops to recruit.
Watch your gold - always keep enough spare gold to recruit about 70% of creatures in your castle or you might end up with well-built castle but no money to recruit troops when enemy comes.
So, the most important thing is: BALANCE BETWEEN TROOPS AND STRUCTURES.

Hero Movement

Distance your hero can travel per day depends on speed of the slowest unit in his army. The slower that unit is, the less distance your hero can travel per day.
Equip scouts with your fastest unit.
If you are in the castle and want to start moving on the next turn, garrison all the slow units, so that hero has only the fastest unit(s). Next day you can give slow units back to your hero and he still will have lots of movement for that day. Slow units can be given to another hero, it doesn't have to be a castle.

To upgrade a creature, it takes double the price difference between creature and it's upgrade. The way to pay the single difference is recruiting them after you upgraded their building.
If wandering creature is trying to run away and you know that you can win with no losses, engage it because you'll get some experience points.
To split creatures: long hold on a creature stack you want to split, drag to the destination slot and update how many creatures you'd like to move.
If you want to destroy a large amount of shooters (ie. elves, ranger etc.), then take a hero equipped with a spell like lightning bolt and 2 flying stacks (prefferably faster than target shooter in order to go first). Bolt the middle stack (hopefully killing it) and fly both stacks into so that it attacks one stack but is touching another one. Now all 4 enemy shooter stacks are engaged. That way the shooters can only stab which does very little damage (unless the shooters have a special abbility of no hand-to-hand penalty).

Chest decision is more complicated than it seems! There are 3 possibilities: 1) 2000g or 1500e. 2) 1500g or 1000e. 3) 1000g or 500e. In number 1 you pay 1.3 gold per 1 experience point. In number 2 you pay 1.5 gold per 1 experience. In number 3 you pay 2 gold per 1 experience. Always take gold from 3rd option. If you want experience, take it from 1st and maybe 2nd option, depending on situation.
Capture every mine even if you have heaps of resources: you can always sell or trade in marketplace.

Newbies! Stay away from shattered ships, and never fight ghosts with level 1 units. Most monsters go for your best, but ghosts deliberately attack the weakest to increase in numbers.
Make multiple heroes in the beginning and hoard all you can without fighting. Usually 1 at home and 2 gathering.