dtgreene: Killing enemies gives you XP, as will certain events (one at the very end of the game gives you a lot of XP that you probably won't use, for example). To reach level 4, you need to have at least 400 XP. If it's like previous Ultima games, only the character who kills the enemy is awarded XP, so you will need to have the Avatar get the XP you need, since she is the only one in the party who can cast spells.
I don't remember if talking to Lord British is necessary in U7 (I happen to not like this particular Ultima, so I don't remember it as well as the others), but I do remember that you get training points when you gain levels. You can boost your stats by finding a trainer and paying for training, provided you have enough training points. Note that each trainer gives you different stat boosts, so find the trainers that you want. (I note that INT and Magic are useful for the Avatar, but not useful for other characters.)
Mustang678: Completing Forge of Virtue will also max out your stats, with your strength rising up to double the max. It is almost cheating
Actually, there's a glitch that lets you get maxed stats without Forge of Virtue, with even more Strength. To do this, just take 6 ((IIRC) doses of Silver Serpent Venom all at once; when they wear off, you will have maxed stats and over 250 Strength. There, is, however, one drawback; the game will treat your maximum health as being negative, which could be a (rather serious) problem.
Taking one more does will fix your Strength, but when it wears off, your stats will go back down to 24.
For those who aren't aware, when you take a dose, your stats increase by 5; when they wear off; your stats decrease by 6, resulting in a net loss. You can, however, use this to your advantage by training Combat or Magic while under the effects; one training point will raise Combat or Magic by half the difference between it and your Dexterity/Intelligence.
Isn't this a lot more interesting than just completing Forge of Virtue?
(Disclaimer: Exult may behave differently here.)