Chris Hansen.
It's a legit question. I usually go full melee and take the enchantments I am lucky enough to loot. Want to manually do it myself this go around.
Even with the name, I had to google him to find out. I have been without TV for 15 years, I'm little out of touch with pop culture. You have way more chance of having me guess a name if you post the picture of a Skyrim Character!
The fastest way to level up enchantment is to go on a crafting spree. I say that because it's a waste of time to level up enchant without leveling up smiting and speech at the same time. I also add Alchemy in my crafting run but you won't need it. You can wait a little before leveling up speech if you want to get back to playing ASAP.
Short story long: start by collecting Iron Ingots. Melt ore to smelt them if needed. Store them until you have enough (100 is a good number). Now, you have to find soul gems. Filled soul gems of the petty kind (cheaper and easier to find). If you can collect 100 that's good but you won't need that many I hope!
Now craft as many iron daggers as you can. Don't forget to sleep in a bed and activate the warrior stone to boost your XP beforehand. Your smiting skill will increase drastically. Once done, time to enchant the daggers. Bring all you can carry to the nearest crafting station and go on a spree. Be sure to switch your standing stone to "mage" as enchant is a mage perk.
Favor "banish" and "soul trap" enchantment, they give very expensive items. Craft as many as you want: 2 or 3 should be enough to go up a level at first but the higher you get, the more you'll need to level up. Craft daggers until you're bored or have reached your goal.
Now, store the daggers you can't carry and carry the rest around for a Merch run. Be sure to change your stone to "thief" since speech is a thief perk. If you know where most specific mechants live, it's just a long trek across Skyrim. You will start leveling up speech, don't be scared to put a perk or two if you want to make the process faster.
It's a little complicated but once you get the hang of it, it's like 2 hours of boring stuff for a whole gameplay of enjoyment!