The first step to victory is building up your party. At the beginning you are fighting against weak monsters. Use the "Repel" or "Undead" spells to easily extinguish the enemies. But leave some for your fighters (if you have characters that can't cast spells) or they won't get any experience points. Gain some levels by talking to Lord British when you have enough EXP and buy better weapons and/or armor with the gold you get after the fights (open the chest always with the spell "Open" - this disables possible traps). Due to your higher levels there will appear stronger monsters/enemies. As soon as you see pirate ships, you have to change your strategy.
Now you must not talk to Lord British any more for new levels (even if you could). This sounds stupid, but you surely recognized that everything you get when gaining a higher level are Hitpoints and not Attribute-Points. And if you would level up any further the enemies would become much too strong for your still "low-attributed" characters. So your most important task now is to fight a pirate ship (pirates), then board the ship and sail into the maelstrom that is somewhere in the ocean (it is moving, so possibly it requires some search). You will wake up in Ambrosia. Get the flowers (do this every time you visit Ambrosia) and visit the shrines to raise attributes (each shrine dedicated to one of the four attributes). The prize for raising one attribute-point for one character is 100GP. So you surely have money for only a few points. Leave Ambrosia by finding the ship in the south and sail back to Sosaria via the maelstrom. Go to "Royal City" and give Sherry the flowers. In return she gives you a Heart Compass. From now on you can leave Ambrosia via Heart Compass (it teleports the party to Lord British's Castle), which is highly recommended.
Okay, now you know how to raise your attributes, but you haven't enough gold for more points and you will need a lot to raise your attributes to a high value. Go to Dawn (it appears only when both moons are "New Moon") which lies 8 squares west and 35 squares south of "Castle British". Go into the Guild and open the most leftern chest. You get the "Gold Pick". Now run out of town. Try to avoid the guards, because they will try to catch you. A good way to avoid being caught is by stopping the time either by a spell or by using the "Sands of Time". Now sail to a small isle near the town of "Gray" and dig with the "Gold Pick". You will find the "Mystic Armor", the best armor in the whole game. Every character-class can wear this thing. So dig with all party-members and equip the armor and sell your old one. You can fight monsters now and gain levels up to level 10 (at this time your possible maximum) and hopefully get some gold. To earn really much money, go to "Devil Guard" (via moongates only) and speak with all people there. One woman will tell you about "bribing" and you can use the command "Bribe" from now on. Go to "Death Gulch", bribe the guards and go to the place were all the treasure is. Steal the treasure and teleport out (because of the guards). Remember to go to Ambrosia to get new flowers and giving them Sherry, when you run out of Heart Compasses. Now you have to travel between Death Gulch and Ambrosia all the time to raise your attributes.
So you are really strong now and you have reached level 10? Then it's time to visit the dungeons. Go to the "Cave of Death" and get the "Mark of the Kings" (every character!). Now you are able to get higher levels (up to the maximum of level 25). Go to level 8 of the dungeon (best by using the spell "Descend") and get the "Silver Pick", then up again (use spell "Ascend"). Dig with the "Silver Pick" on an isle near the town of Fawn and find the "Mystic Sword". This is the best (melee) weapon in the game and similar to the "Mystic Armor" it can be used by every character so equip everyone with a "Mystic Sword" (except if you want to use long-range weapons). Fight monsters and raise every character to level 25 (and keep raising your attributes to maximum). Perhaps the fastest and easiest way to get more EXP is to fight red town guards, because they come in groups of 8, give you 15 EXP and are easy to beat (for a strong party). And they are always "at hand" if you need a good fight. Now it's getting more interesting. Go to the "Cave of Moon" and get the "Mark of Fire" (and if you are interested visit the Timelord to get a hint for the endgame, but you don't have to do this, if you use this walkthrough). Now go to the "Cave of Sol" and get the "Mark of Snake" and finally in the "Cave of Fool" the "Mark of Force". Travel to "Yew" and speak with the priest in the temple. You get the command "Pray". Use it in the "Circle of Light" and you get the "Silver Horn". Travel to every shrine in Ambrosia, use "Pray" and get the 4 cards. Sail to Exodus' Castle and blow the "Silver Horn". The snake disappears. Good, now you can enter the castle.
The Endgame: I hope your characters have full Magic-Points and Hit-Points. You will have to fight your way to Exodus (strong monsters!). In the north part of the castle fight the "Floor" and you are standing in front of Exodus. Use the command "Pray" and use the cards (combination: Love, Sun, Moons, Death). Take the ankh. Exodus is destroyed and the castle is shaking. Leave it immediately and.... watch the credits.