Beginner's Tricks

These are some basic things all players should grasp in their "dockbaby" stage:

Balming. Balms of Gilead are potions that restore Hit Points. They are sold in every town. It is very hard to survive without them.
Recalling. Rings of recall allow instantaneous teleport to the place you have set them (the place you were when you put them on). They can really save your life when the hunt turns bad. They can be bought in every town, or crafted by Thieves.
Training. Spending money at the trainer will make your skills increase faster in the future ; up to 100% faster when fully trained. You can train both weapons and magic, at the appropriate trainer.
To split coins, hold [shift] and drag them to a counter or empty slot. A prompt will pop-up asking how much you want to separate.

Advanced tips

Balm riding. Balms heal you for a large number of rounds until you are fully healed, then stops. Learning when to balm is important. If you wait a bit more before drinking it, you take a little risk, but you also increase the heal duration.
Dark hexes. Jumping into hexes that are not visible from where you are is a good way to escape danger. Be careful though not to run into a wall or into a bigger critter.

You can change your Screen Resolution from the Login Screen. The resolutions available will depend on your video card.