Note: This walkthrough is rather short, but so is the game. If you are fast you can beat it in one afternoon. And remember to save often!
Your first task is to equip and level up your character. Go into the nearest town and buy better weapons, food and armour. It's time to increase your experience points by fighting monsters. This part of the game takes the most time. The best way to get experience points is to fight monsters in dungeons, because when you leave the dungeon, you get back a special amount of HP based on the number of monsters you killed. When you are lucky you have more HP after your visit in the dungeon than before. So there is no need to spend your money for buying HP at the castles. So go into the dungeons (best is you visit only level 1 and 2) and fight, fight, fight. If you have the money or you need food go back to town and buy better armour, food, weapons (a bow is a good weapon in this part of the game) or a horse. If you don't get bored soon (or killed) you can get the maximum of experience points and a level 10 character with a good amount of HP in less than 2 hours. This makes the rest of the game much easier.
Next step is to explore the world and raising your attributes. Buy an aircar and travel to the castles to get quests. Four quests are to find a specific location and four other quests are to kill a specific monsters which can be found in deeper dungeon levels. The locations are sign posts which are on islands around the continents. These are also the places where you can raise your attributes. Raise all your attributes to the maximum and return to the kings, who give you additional "Strength". One sign post is special, because you can get weapons here. Visit this sign post until you get the best weapon in the game, the "Blaster". Equip this weapon and sell the others. More about the sign posts can be read in the "Sign Posts-Section".
If you have equipped a "Blaster", a "Reflect Suit", and bought a huge amount of "Ladder Down" and "Ladder Up" spells, you are ready to go after the quests to kill the monsters. Enter a dungeon and kill the monsters. Firstly kill a "Gelatinous Cube" (can be found on level 3+4) for the Lord in the "Castle of the Lost King". As a reward you will get a "Red Gem". Then kill a "Carrion Creeper" (can be found on level 5+6) for the Lord in "Castle Rondorin". As a reward you will get another gem (green). Do so again with a Lich (level 7+8) for the Lord in the "Black Dragon's Castle" (blue gem) and with a Balron (level 9+10) for the Lord in the "Castle of Shamino" (white gem). To reach and leave the deeper levels quickly, use the "Ladder Down" and "Ladder Up" spells!
Buy a "Vacuum Suit" and "Shuttle" now, because it's time to enter space and become a "Space Ace". Wear the "Vacuum Suit" before boarding the "Shuttle" and make sure you bring enough coins along!! In Space, shoot down 20 hostile spaceships to become a "Space Ace". More information about this part of the game can be found in the "Space-Section". Back on Sosaria visit the "Castle of Lord British" (or another castle that looks the same) and kill the jester. You get a key. With this key walk to the prison and free the princess. After killing the jester you have to fight the guards so make sure you have enough HP. Leave the castle with the princess. Since you are a "Space Ace" she tells you of a "Time Machine" hidden somewhere. You can find it near a "Sign Post".
Now it's time to end the reign of the evil Mondain! Before you enter the "Time Machine" make sure that you have full HP. Enter the "Time Machine" and since you have the four gems you can use it to travel through time to Mondain the evil wizard. You see Mondain standing near a gem. Take the gem (press "G" on keyboard while standing near it) and you automatically destroy it. Ouch!, that costed a lot of HP! Now fight Mondain. When you have hit him several times he shapeshifts into a bat and tries to flee. Follow him and shoot him with your blaster when in range. After some time you should have successfully killed him and saved the world.