Put a character with sufficient tailoring to make the desired item into the faction. (Tailoring does not have to be GM. If it is less than GM, you won't get a maker's mark on the item.) Make sure your faction controls one of the faction towns that has a tailor shop in it. Rustle up some silver. Have the tailor go park herself/himself in the tailor shop of the town your faction controls. Make the item you want. If the tailor produces something of exceptional quality, a gump will immediately appear asking if you want the item to be hued in one of the two faction colors (e.g., blue or gold for TB) and will tell you what the silver cost will be and how much silver the tailor has in his/her backpack. The item will change to the selected color and show that it is Blessed and a Faction Item. I believe it will stay blessed and faction-hued for 21 days. Note that if you don't have enough silver in your pack to hue/bless the item, you will NOT see the special gump even if you made an exceptional quality item and were in the proper location.
My less-than-GM tailor on GL was able to make a robe, cloak, plain dress, half apron, full apron, sandals. Probably could have made more but I hated wasting the silver. I also had her make a shield. It came out with a maker's mark because she's got slightly more than GM smithing.
There's more specific information about faction crafting on the UO site here:
http://www.uoherald.com/guide/guide.php?guideId=212.
If you don't want to try to get into your faction's base to see if your faction controls a specific town, you can go to the sigil post in the town you're wondering about and look at the color of the post. The color of the post will indicate which faction currently controls that town (i.e., red = Minax; black = SL; purple = TB; blue = COM).