On the second floor, take the stairs in the southwest corner to the third floor. Then, take the other stairs back down to the second floor, and get treasure T2.
Now go back to the second floor and take the stairs in the northeast corner. Take the stairs down to get treasure T3 - the Tower Key! Then go back to the third floor, and enter the room in the middle of that floor.
Take the stairs up to the fourth floor and get the three treasures there. (Oh, by the way, one of them is a Mimic. Not to worry though, if you have the Iron Bow and Iron Sword you should easily defeat it in one round.)
Now, go back and take the only stairs you haven't taken yet. Follow the path to the west, and take these stairs up to the fifth floor, and your first boss battle.
Mad Ruler, Skeleton x2
Approach the enemy in the middle of the 5th floor, and select "No."
This will launch the battle against the Tower Master.
Kill the Skeletons first.
Otherwise, there's a chance they'll Cure themselves, and the battle will drag on longer than necessary.
Now use Poison on the Mad Ruler, then attack him regularly and heal your party as needed.
When the battle's over, go back to the first floor and get the last treasure, then go to Temple Town where you can now recruit Temi, and change classes. Except that you still can't change classes, because most classes require that you obtain a specific item first, and the only one that is available right now is for Bruce, and only after his Archer level reaches 15...
But the good news is that by now, Blont should have learned Warp, meaning from this point forward in the game, you can automatically warp back to Temple Town at any time (as long as Blont has enough MP). So for now, it's on with the story!
As soon as you're ready, your next destination is the Mountain Village. And the easiest way to get there is to warp to Northwest Town, and then walk to the southwest.