In the 2d client, to examine the current status of your virtues, double click the pentagram-looking thing right at the top of your paperdoll. A weird gump will pop up with large circles on it. Each large circle corresponds with the status of one virtue, and if you actually have any credit built up on any of the virtues, the corresponding circle will be colored in some way (the color hue is brighter or lower based upon the "tier" of the virtue you have earned, more on that coming in a sec). For honor, the honor circle will have purple in it.
There's 4 tiers to honor - nothing, seeker, follower, and knight. To advance through each one, you do the honorable acts, and each act adds just a little bit of honor. Over time, you progress through seeker, into follower, and then maybe to knight.
On that circle filled gump, click the blue 'status' button on the bottom of that gump, and then click the blue dot thingie for honor, and you'll see how many colored 'dots' into your particular form (nothing, seeker, follower) you are. Red dots mean unfilled dots. As you do honorable acts, you will see the blue dots replace the reds ones moving from left to right, then when the page is completely full, it will pop you one tier higher, and reset your dots back to none. It takes a number of honorable acts to move even one dot, it's not a 1 to 1 ratio.
To build honor, you make a UO macro that says:
Invoke virtue, Honor.
And then, when you are about to attack an undamaged monster, you activate that macro. A targeting cursor will come up. You select the monster (or its health bar or its name tag, whatever), and then you kill the monster. You'll see a message saying that you gained honor, assuming you did.
And you do that over and over again, and you will see the blue dots increase.
The benefit of honor, once you get to seeker or follower or knight, is that you can use that macro, and then instead of targeting the monster, you target yourself. All the monsters that are around you will ignore you for a little while. When you're only seeker, it doesn't last real long; when you're follower, it lasts a fair amount of time so you can get things done; and if you managed to hit knight, that sh*t seems to last a long time. Maintaining knight is a pain in the ass though, if you actually use your honor somewhat regularly.