What you need is to have a very high enchant skill and there are a few ways to achieve that. First you need to buy the Masterful Transfiguring Wisdom spell in either Mournhold or Skaal Village on Solstheim.
Then goto to an enchanter e.g http://www.uesp.net/wiki/Morrowind:Galbedir/http://www.uesp.net/wiki/Morrowind:Miun-Gei/http://www.uesp.net/wiki/Morrowind:Llether_Vari and pay them for their services, but I strongly advice you to do what I do in-game.
Remember the only spell effect I know of that's useless to have as a constant effect is spell absorption, spell reflect IIRC due to the use of high enchantment points cost for each points e.g 50 enchantment points for only 1 pts of spell absorption - constant effect.
Start to create a simple enchanted ring with 15 pts for 10 seconds I think of the Fortify Skill (Enchant) and an expensive ring plus a filled petty soul gem (cliff racers or shalk will due) that have 30 enchantment points are needed. Once you have done that then use the ring to improve your enchant skill in order to create a better Fortify Enchant Skill ring, which now can be almost anything I mean you don't have an expensive amulet/ring anymore.
I always do that in my game and later in-game I could improve my enchant skill just below 500 of the enchant skill with a couple of amulets/rings, so when you can improve your enchant skill that high then you can enchant your own items with constant effect without fuss.