From the main menu, press the A key to generate a new character. You will first need to choose how to allocate points to your attributes, after which you will need to choose your race, sex, class and name.
Once you are back at the main menu, press the B key and proceed to load the character you have just created.
You start off just east of Britain and the Castle of Lord British. You have just 150 hits, 200 food, 100 coins, and no experience at all. Your first priority is to go to Britain and buy a decent weapon and some armour to allow you to survive. A mace and a chain mail are good for starters.
In the beginning, you're going to be watching your Hits and Food a lot, because if either of those reaches zero, you're dead. You're going to want to increase all your vitals (hits, food, experience and coins) before trying to embark upon any quest. You get coins and experience by killing monsters. You can then use those coins to buy food (from grocers) and hits (from kings).
You can kill monsters in the overworld or in dungeons. Dungeoneering has the advantage that you'll get additional hit points when you leave the dungeon. However, you will want to do this gradually; the enemies in dungeons become more powerful after every two levels, and the deeper you go, the more difficult it becomes to find your way back out (although Ladder Up spells can be very useful in this regard).
As the game progresses and you become more powerful, you'll want to buy better weapons (focus on the ranged ones) and armour (go for a Reflect Suit), as well as spells and transport (an aircar is great) to make your life easier.
You are initially confined to the Lands of Lord British, but once you have enough money, you can buy transport from shops in order to cross over into the other three continents. An aircar is a pretty good choice, since it allows you to fly over land and sea (although not into woods), it can fire lasers at a distance, and it's fast so you can outrun your enemies and save on the food you consume.
There are four continents, and each continent has two castles each ruled by a king. Four of the kings will give you a quest that involves going down into any dungeon and slaying a particular monster. When you do that and go back to the king, he will give you some useful advice and a gem that you will later need to use the time machine. The other four kings will send you to sign posts across the world, and this will allow you to boost your attributes and acquire a few useful items, but their quests are optional.
The Lost King wants you to kill a gelatinous cube. You can find one on level 3 or 4 of any dungeon. Beware, though: these creatures have the ability to dissolve your armour, so remove it before you descend into level 3 by readying your skin as your armour.
Once you slay a gelatinous cube and go back to the Lost King, he will give you a red gem and tell you that it is one of four gems needed to operate a time machine.
Kill a carrion creeper (dungeon levels 5 or 6) for the King at Castle Rondorin. When you go back to him, he gives you a green gem together with the advice that a time machine is essential for your victory against Mondain.
The King at the Black Dragon's Castle needs you to kill a lich. To do that, go down into any dungeon and find one on the 7th or 8th level. Once you have done the job, go back to the king, who gives you a blue gem and tells you that princesses are particularly helpful to a space ace.
Your most dangerous quest comes from the Castle of Shamino. To satisfy the king, you must descend into the deepest levels (9 or 10) of any dungeon and slay a balron. The monsters down here are pretty tough, and it can take a while to find your way back to the surface, so make sure you have plenty of hit points and Ladder Up spells before you embark on such an undertaking.
At this point you'll want to kill a bunch of monsters and save some money. When you can afford it, and have about 2000 coins to spare, buy a Shuttle. You will also need to be wearing either a vacuum suit or a reflect suit before you lift off, otherwise you won't survive the trip.
Once you're in space, dock the shuttle carefully at the space station, and change to a tougher ship - you're going to be hunting aliens. Docking at the space station bears a charge of 500 coins, and is necessary whenever you want to refuel your ship or switch to a different one (e.g. only the shuttle can get you back to Sosaria in one piece).
Use the I key to get a map of the sectors around Sosaria. Orient your ship in the direction you want to go while you're in top view. Then, switch to front view with the V key, and then hit H to hyperjump into an adjacent sector.
You want to target those sectors that are marked with a sort of "H" - this means there are alien fighters there. Go through the sectors containing aliens and hunt them down, using arrow keys and Space to target alien fighters and F to fire your lasers at them. Once you take down 20 alien fighters, you achieve the rank of Space Ace.
Recalling the words of the King at the Black Dragon's Castle, you can now enlist the aid of a princess by freeing her from any castle. You do this by murdering the jester in cold blood in order to get a key, and then attempting to unlock her cell with it (it's not always the right key). If it works, you have to kill or elude the guards while she follows you outside. Once you exit the castle, she rewards you and points you to a time machine "far to the northwest".
Head northwest and find the time machine. Get into it and you will be taken straight to Mondain!
The time machine takes you to back to the time when Mondain was still crafting his Gem of Immortality, and thus he is vulnerable.
Walk over to his gem and Get it in order to destroy it. The backlash will cause significant damage to you, but Mondain may now be killed. Hit him repeatedly with your best weapon.
After a bit, he turns into a bat and tries to run away. Corner him and keep hitting him until he dies.