MMORPG.com's V D has provided us with this guide to the Archery Training Skill in Ultima Online.

Archery is for ranged fighting. This is good, because you can do damage to your opponent and stay safe unlike melee fighters. The difficulty is making sure you are far away enough to reload safely, but not so far away that your shooting range is limited.

As an archer you will need a ridiculous amount of arrows or bolts. If you train in fletching you will have a 99% chance of success to make these with only 30% skill level. You will need to gather wood from the forest and kill birdies or harpies for feathers. Also, centaurs, ratmen mages, and juka lords are usually good sources of free arrows after you kindly explain you would like them to die and give you all their belongings. Alternatively, you could buy arrows and save time. I personally recommend doing just that!

Read the Ultima Online Archery Skill Guide